# Richard J. Mathar, Fri Aug 3 15:57:57 MEST 2007 Zernike Polynomials R(n,m,r): R(0,0,r) = 1 R(1,1,r) = r R(2,0,r) = 2*r^2 - 1 R(2,2,r) = r^2 R(3,1,r) = 3*r^3 - 2*r R(3,3,r) = r^3 R(4,0,r) = 6*r^4 - 6*r^2 + 1 R(4,2,r) = 4*r^4 - 3*r^2 R(4,4,r) = r^4 R(5,1,r) = 10*r^5 - 12*r^3 + 3*r R(5,3,r) = 5*r^5 - 4*r^3 R(5,5,r) = r^5 R(6,0,r) = 20*r^6 - 30*r^4 + 12*r^2 - 1 R(6,2,r) = 15*r^6 - 20*r^4 + 6*r^2 R(6,4,r) = 6*r^6 - 5*r^4 R(6,6,r) = r^6 R(7,1,r) = 35*r^7 - 60*r^5 + 30*r^3 - 4*r R(7,3,r) = 21*r^7 - 30*r^5 + 10*r^3 R(7,5,r) = 7*r^7 - 6*r^5 R(7,7,r) = r^7 R(8,0,r) = 70*r^8 - 140*r^6 + 90*r^4 - 20*r^2 + 1 R(8,2,r) = 56*r^8 - 105*r^6 + 60*r^4 - 10*r^2 R(8,4,r) = 28*r^8 - 42*r^6 + 15*r^4 R(8,6,r) = 8*r^8 - 7*r^6 R(8,8,r) = r^8 R(9,1,r) = 126*r^9 - 280*r^7 + 210*r^5 - 60*r^3 + 5*r R(9,3,r) = 84*r^9 - 168*r^7 + 105*r^5 - 20*r^3 R(9,5,r) = 36*r^9 - 56*r^7 + 21*r^5 R(9,7,r) = 9*r^9 - 8*r^7 R(9,9,r) = r^9 R(10,0,r) = 252*r^10 - 630*r^8 + 560*r^6 - 210*r^4 + 30*r^2 - 1 R(10,2,r) = 210*r^10 - 504*r^8 + 420*r^6 - 140*r^4 + 15*r^2 R(10,4,r) = 120*r^10 - 252*r^8 + 168*r^6 - 35*r^4 R(10,6,r) = 45*r^10 - 72*r^8 + 28*r^6 R(10,8,r) = 10*r^10 - 9*r^8 R(10,10,r) = r^10 R(11,1,r) = 462*r^11 - 1260*r^9 + 1260*r^7 - 560*r^5 + 105*r^3 - 6*r R(11,3,r) = 330*r^11 - 840*r^9 + 756*r^7 - 280*r^5 + 35*r^3 R(11,5,r) = 165*r^11 - 360*r^9 + 252*r^7 - 56*r^5 R(11,7,r) = 55*r^11 - 90*r^9 + 36*r^7 R(11,9,r) = 11*r^11 - 10*r^9 R(11,11,r) = r^11 R(12,0,r) = 924*r^12 - 2772*r^10 + 3150*r^8 - 1680*r^6 + 420*r^4 - 42*r^2 + 1 R(12,2,r) = 792*r^12 - 2310*r^10 + 2520*r^8 - 1260*r^6 + 280*r^4 - 21*r^2 R(12,4,r) = 495*r^12 - 1320*r^10 + 1260*r^8 - 504*r^6 + 70*r^4 R(12,6,r) = 220*r^12 - 495*r^10 + 360*r^8 - 84*r^6 R(12,8,r) = 66*r^12 - 110*r^10 + 45*r^8 R(12,10,r) = 12*r^12 - 11*r^10 R(12,12,r) = r^12 R(13,1,r) = 1716*r^13 - 5544*r^11 + 6930*r^9 - 4200*r^7 + 1260*r^5 - 168*r^3 + 7*r R(13,3,r) = 1287*r^13 - 3960*r^11 + 4620*r^9 - 2520*r^7 + 630*r^5 - 56*r^3 R(13,5,r) = 715*r^13 - 1980*r^11 + 1980*r^9 - 840*r^7 + 126*r^5 R(13,7,r) = 286*r^13 - 660*r^11 + 495*r^9 - 120*r^7 R(13,9,r) = 78*r^13 - 132*r^11 + 55*r^9 R(13,11,r) = 13*r^13 - 12*r^11 R(13,13,r) = r^13 R(14,0,r) = 3432*r^14 - 12012*r^12 + 16632*r^10 - 11550*r^8 + 4200*r^6 - 756*r^4 + 56*r^2 - 1 R(14,2,r) = 3003*r^14 - 10296*r^12 + 13860*r^10 - 9240*r^8 + 3150*r^6 - 504*r^4 + 28*r^2 R(14,4,r) = 2002*r^14 - 6435*r^12 + 7920*r^10 - 4620*r^8 + 1260*r^6 - 126*r^4 R(14,6,r) = 1001*r^14 - 2860*r^12 + 2970*r^10 - 1320*r^8 + 210*r^6 R(14,8,r) = 364*r^14 - 858*r^12 + 660*r^10 - 165*r^8 R(14,10,r) = 91*r^14 - 156*r^12 + 66*r^10 R(14,12,r) = 14*r^14 - 13*r^12 R(14,14,r) = r^14 R(15,1,r) = 6435*r^15 - 24024*r^13 + 36036*r^11 - 27720*r^9 + 11550*r^7 - 2520*r^5 + 252*r^3 - 8*r R(15,3,r) = 5005*r^15 - 18018*r^13 + 25740*r^11 - 18480*r^9 + 6930*r^7 - 1260*r^5 + 84*r^3 R(15,5,r) = 3003*r^15 - 10010*r^13 + 12870*r^11 - 7920*r^9 + 2310*r^7 - 252*r^5 R(15,7,r) = 1365*r^15 - 4004*r^13 + 4290*r^11 - 1980*r^9 + 330*r^7 R(15,9,r) = 455*r^15 - 1092*r^13 + 858*r^11 - 220*r^9 R(15,11,r) = 105*r^15 - 182*r^13 + 78*r^11 R(15,13,r) = 15*r^15 - 14*r^13 R(15,15,r) = r^15 R(16,0,r) = 12870*r^16 - 51480*r^14 + 84084*r^12 - 72072*r^10 + 34650*r^8 - 9240*r^6 + 1260*r^4 - 72*r^2 + 1 R(16,2,r) = 11440*r^16 - 45045*r^14 + 72072*r^12 - 60060*r^10 + 27720*r^8 - 6930*r^6 + 840*r^4 - 36*r^2 R(16,4,r) = 8008*r^16 - 30030*r^14 + 45045*r^12 - 34320*r^10 + 13860*r^8 - 2772*r^6 + 210*r^4 R(16,6,r) = 4368*r^16 - 15015*r^14 + 20020*r^12 - 12870*r^10 + 3960*r^8 - 462*r^6 R(16,8,r) = 1820*r^16 - 5460*r^14 + 6006*r^12 - 2860*r^10 + 495*r^8 R(16,10,r) = 560*r^16 - 1365*r^14 + 1092*r^12 - 286*r^10 R(16,12,r) = 120*r^16 - 210*r^14 + 91*r^12 R(16,14,r) = 16*r^16 - 15*r^14 R(16,16,r) = r^16 R(17,1,r) = 24310*r^17 - 102960*r^15 + 180180*r^13 - 168168*r^11 + 90090*r^9 - 27720*r^7 + 4620*r^5 - 360*r^3 + 9*r R(17,3,r) = 19448*r^17 - 80080*r^15 + 135135*r^13 - 120120*r^11 + 60060*r^9 - 16632*r^7 + 2310*r^5 - 120*r^3 R(17,5,r) = 12376*r^17 - 48048*r^15 + 75075*r^13 - 60060*r^11 + 25740*r^9 - 5544*r^7 + 462*r^5 R(17,7,r) = 6188*r^17 - 21840*r^15 + 30030*r^13 - 20020*r^11 + 6435*r^9 - 792*r^7 R(17,9,r) = 2380*r^17 - 7280*r^15 + 8190*r^13 - 4004*r^11 + 715*r^9 R(17,11,r) = 680*r^17 - 1680*r^15 + 1365*r^13 - 364*r^11 R(17,13,r) = 136*r^17 - 240*r^15 + 105*r^13 R(17,15,r) = 17*r^17 - 16*r^15 R(17,17,r) = r^17 R(18,0,r) = 48620*r^18 - 218790*r^16 + 411840*r^14 - 420420*r^12 + 252252*r^10 - 90090*r^8 + 18480*r^6 - 1980*r^4 + 90*r^2 - 1 R(18,2,r) = 43758*r^18 - 194480*r^16 + 360360*r^14 - 360360*r^12 + 210210*r^10 - 72072*r^8 + 13860*r^6 - 1320*r^4 + 45*r^2 R(18,4,r) = 31824*r^18 - 136136*r^16 + 240240*r^14 - 225225*r^12 + 120120*r^10 - 36036*r^8 + 5544*r^6 - 330*r^4 R(18,6,r) = 18564*r^18 - 74256*r^16 + 120120*r^14 - 100100*r^12 + 45045*r^10 - 10296*r^8 + 924*r^6 R(18,8,r) = 8568*r^18 - 30940*r^16 + 43680*r^14 - 30030*r^12 + 10010*r^10 - 1287*r^8 R(18,10,r) = 3060*r^18 - 9520*r^16 + 10920*r^14 - 5460*r^12 + 1001*r^10 R(18,12,r) = 816*r^18 - 2040*r^16 + 1680*r^14 - 455*r^12 R(18,14,r) = 153*r^18 - 272*r^16 + 120*r^14 R(18,16,r) = 18*r^18 - 17*r^16 R(18,18,r) = r^18 R(19,1,r) = 92378*r^19 - 437580*r^17 + 875160*r^15 - 960960*r^13 + 630630*r^11 - 252252*r^9 + 60060*r^7 - 7920*r^5 + 495*r^3 - 10*r R(19,3,r) = 75582*r^19 - 350064*r^17 + 680680*r^15 - 720720*r^13 + 450450*r^11 - 168168*r^9 + 36036*r^7 - 3960*r^5 + 165*r^3 R(19,5,r) = 50388*r^19 - 222768*r^17 + 408408*r^15 - 400400*r^13 + 225225*r^11 - 72072*r^9 + 12012*r^7 - 792*r^5 R(19,7,r) = 27132*r^19 - 111384*r^17 + 185640*r^15 - 160160*r^13 + 75075*r^11 - 18018*r^9 + 1716*r^7 R(19,9,r) = 11628*r^19 - 42840*r^17 + 61880*r^15 - 43680*r^13 + 15015*r^11 - 2002*r^9 R(19,11,r) = 3876*r^19 - 12240*r^17 + 14280*r^15 - 7280*r^13 + 1365*r^11 R(19,13,r) = 969*r^19 - 2448*r^17 + 2040*r^15 - 560*r^13 R(19,15,r) = 171*r^19 - 306*r^17 + 136*r^15 R(19,17,r) = 19*r^19 - 18*r^17 R(19,19,r) = r^19 R(20,0,r) = 184756*r^20 - 923780*r^18 + 1969110*r^16 - 2333760*r^14 + 1681680*r^12 - 756756*r^10 + 210210*r^8 - 34320*r^6 + 2970*r^4 - 110*r^2 + 1 R(20,2,r) = 167960*r^20 - 831402*r^18 + 1750320*r^16 - 2042040*r^14 + 1441440*r^12 - 630630*r^10 + 168168*r^8 - 25740*r^6 + 1980*r^4 - 55*r^2 R(20,4,r) = 125970*r^20 - 604656*r^18 + 1225224*r^16 - 1361360*r^14 + 900900*r^12 - 360360*r^10 + 84084*r^8 - 10296*r^6 + 495*r^4 R(20,6,r) = 77520*r^20 - 352716*r^18 + 668304*r^16 - 680680*r^14 + 400400*r^12 - 135135*r^10 + 24024*r^8 - 1716*r^6 R(20,8,r) = 38760*r^20 - 162792*r^18 + 278460*r^16 - 247520*r^14 + 120120*r^12 - 30030*r^10 + 3003*r^8 R(20,10,r) = 15504*r^20 - 58140*r^18 + 85680*r^16 - 61880*r^14 + 21840*r^12 - 3003*r^10 R(20,12,r) = 4845*r^20 - 15504*r^18 + 18360*r^16 - 9520*r^14 + 1820*r^12 R(20,14,r) = 1140*r^20 - 2907*r^18 + 2448*r^16 - 680*r^14 R(20,16,r) = 190*r^20 - 342*r^18 + 153*r^16 R(20,18,r) = 20*r^20 - 19*r^18 R(20,20,r) = r^20 R(21,1,r) = 352716*r^21 - 1847560*r^19 + 4157010*r^17 - 5250960*r^15 + 4084080*r^13 - 2018016*r^11 + 630630*r^9 - 120120*r^7 + 12870*r^5 - 660*r^3 + 11*r R(21,3,r) = 293930*r^21 - 1511640*r^19 + 3325608*r^17 - 4084080*r^15 + 3063060*r^13 - 1441440*r^11 + 420420*r^9 - 72072*r^7 + 6435*r^5 - 220*r^3 R(21,5,r) = 203490*r^21 - 1007760*r^19 + 2116296*r^17 - 2450448*r^15 + 1701700*r^13 - 720720*r^11 + 180180*r^9 - 24024*r^7 + 1287*r^5 R(21,7,r) = 116280*r^21 - 542640*r^19 + 1058148*r^17 - 1113840*r^15 + 680680*r^13 - 240240*r^11 + 45045*r^9 - 3432*r^7 R(21,9,r) = 54264*r^21 - 232560*r^19 + 406980*r^17 - 371280*r^15 + 185640*r^13 - 48048*r^11 + 5005*r^9 R(21,11,r) = 20349*r^21 - 77520*r^19 + 116280*r^17 - 85680*r^15 + 30940*r^13 - 4368*r^11 R(21,13,r) = 5985*r^21 - 19380*r^19 + 23256*r^17 - 12240*r^15 + 2380*r^13 R(21,15,r) = 1330*r^21 - 3420*r^19 + 2907*r^17 - 816*r^15 R(21,17,r) = 210*r^21 - 380*r^19 + 171*r^17 R(21,19,r) = 21*r^21 - 20*r^19 R(21,21,r) = r^21 R(22,0,r) = 705432*r^22 - 3879876*r^20 + 9237800*r^18 - 12471030*r^16 + 10501920*r^14 - 5717712*r^12 + 2018016*r^10 - 450450*r^8 + 60060*r^6 - 4290*r^4 + 132*r^2 - 1 R(22,2,r) = 646646*r^22 - 3527160*r^20 + 8314020*r^18 - 11085360*r^16 + 9189180*r^14 - 4900896*r^12 + 1681680*r^10 - 360360*r^8 + 45045*r^6 - 2860*r^4 + 66*r^2 R(22,4,r) = 497420*r^22 - 2645370*r^20 + 6046560*r^18 - 7759752*r^16 + 6126120*r^14 - 3063060*r^12 + 960960*r^10 - 180180*r^8 + 18018*r^6 - 715*r^4 R(22,6,r) = 319770*r^22 - 1627920*r^20 + 3527160*r^18 - 4232592*r^16 + 3063060*r^14 - 1361360*r^12 + 360360*r^10 - 51480*r^8 + 3003*r^6 R(22,8,r) = 170544*r^22 - 813960*r^20 + 1627920*r^18 - 1763580*r^16 + 1113840*r^14 - 408408*r^12 + 80080*r^10 - 6435*r^8 R(22,10,r) = 74613*r^22 - 325584*r^20 + 581400*r^18 - 542640*r^16 + 278460*r^14 - 74256*r^12 + 8008*r^10 R(22,12,r) = 26334*r^22 - 101745*r^20 + 155040*r^18 - 116280*r^16 + 42840*r^14 - 6188*r^12 R(22,14,r) = 7315*r^22 - 23940*r^20 + 29070*r^18 - 15504*r^16 + 3060*r^14 R(22,16,r) = 1540*r^22 - 3990*r^20 + 3420*r^18 - 969*r^16 R(22,18,r) = 231*r^22 - 420*r^20 + 190*r^18 R(22,20,r) = 22*r^22 - 21*r^20 R(22,22,r) = r^22 Jacobi Polynomials G(n,2,2,r) in terms of powers: G(0,2,2,r)= 1 G(1,2,2,r)= r - 2/3 G(2,2,2,r)= r^2 - 6/5*r + 3/10 G(3,2,2,r)= r^3 - 12/7*r^2 + 6/7*r - 4/35 G(4,2,2,r)= r^4 - 20/9*r^3 + 5/3*r^2 - 10/21*r + 5/126 G(5,2,2,r)= r^5 - 30/11*r^4 + 30/11*r^3 - 40/33*r^2 + 5/22*r - 1/77 G(6,2,2,r)= r^6 - 42/13*r^5 + 105/26*r^4 - 350/143*r^3 + 105/143*r^2 - 14/143*r + 7/1716 G(7,2,2,r)= r^7 - 56/15*r^6 + 28/5*r^5 - 56/13*r^4 + 70/39*r^3 - 56/143*r^2 + 28/715*r - 8/6435 G(8,2,2,r)= r^8 - 72/17*r^7 + 126/17*r^6 - 588/85*r^5 + 63/17*r^4 - 252/221*r^3 + 42/221*r^2 - 36/2431*r + 9/24310 G(9,2,2,r)= r^9 - 90/19*r^8 + 180/19*r^7 - 3360/323*r^6 + 2205/323*r^5 - 882/323*r^4 + 210/323*r^3 - 360/4199*r^2 + 45/8398*r - 5/46189 G(10,2,2,r)= r^10 - 110/21*r^9 + 165/14*r^8 - 1980/133*r^7 + 220/19*r^6 - 1848/323*r^5 + 1155/646*r^4 - 110/323*r^3 + 165/4522*r^2 - 55/29393*r + 11/352716 G(11,2,2,r)= r^11 - 132/23*r^10 + 330/23*r^9 - 3300/161*r^8 + 2970/161*r^7 - 4752/437*r^6 + 1848/437*r^5 - 7920/7429*r^4 + 2475/14858*r^3 - 110/7429*r^2 + 33/52003*r - 6/676039 G(12,2,2,r)= r^12 - 156/25*r^11 + 429/25*r^10 - 3146/115*r^9 + 1287/46*r^8 - 15444/805*r^7 + 5148/575*r^6 - 30888/10925*r^5 + 1287/2185*r^4 - 572/7429*r^3 + 429/74290*r^2 - 39/185725*r + 13/5200300 G(13,2,2,r)= r^13 - 182/27*r^12 + 182/9*r^11 - 8008/225*r^10 + 11011/270*r^9 - 11011/345*r^8 + 2002/115*r^7 - 2288/345*r^6 + 1001/575*r^5 - 2002/6555*r^4 + 2002/58995*r^3 - 728/334305*r^2 + 91/1337220*r - 7/10029150 G(14,2,2,r)= r^14 - 210/29*r^13 + 1365/58*r^12 - 11830/261*r^11 + 5005/87*r^10 - 22022/435*r^9 + 11011/348*r^8 - 9438/667*r^7 + 3003/667*r^6 - 2002/2001*r^5 + 1001/6670*r^4 - 182/12673*r^3 + 91/114057*r^2 - 14/646323*r + 1/5170584 G(15,2,2,r)= r^15 - 240/31*r^14 + 840/31*r^13 - 50960/899*r^12 + 70980/899*r^11 - 208208/2697*r^10 + 440440/8091*r^9 - 25168/899*r^8 + 9438/899*r^7 - 176176/62031*r^6 + 56056/103385*r^5 - 1456/20677*r^4 + 364/62031*r^3 - 112/392863*r^2 + 8/1178589*r - 16/300540195 G(16,2,2,r)= r^16 - 272/33*r^15 + 340/11*r^14 - 23800/341*r^13 + 108290/1023*r^12 - 1126216/9889*r^11 + 80444/899*r^10 - 1264120/24273*r^9 + 60775/2697*r^8 - 19448/2697*r^7 + 68068/40455*r^6 - 86632/310155*r^5 + 21658/682341*r^4 - 4760/2047023*r^3 + 68/682341*r^2 - 136/64822395*r + 17/1166803110 G(17,2,2,r)= r^17 - 306/35*r^16 + 1224/35*r^15 - 6528/77*r^14 + 1530/11*r^13 - 55692/341*r^12 + 241332/1705*r^11 - 413712/4495*r^10 + 284427/6293*r^9 - 316030/18879*r^8 + 29172/6293*r^7 - 21216/22475*r^6 + 3094/22475*r^5 - 1428/103385*r^4 + 204/227447*r^3 - 272/7960645*r^2 + 51/79606450*r - 3/756261275 G(18,2,2,r)= r^18 - 342/37*r^17 + 2907/74*r^16 - 131784/1295*r^15 + 46512/259*r^14 - 93024/407*r^13 + 88179/407*r^12 - 1965132/12617*r^11 + 491283/5735*r^10 - 1200914/33263*r^9 + 5404113/465682*r^8 - 655044/232841*r^7 + 16796/33263*r^6 - 54264/831575*r^5 + 969/166315*r^4 - 1292/3825245*r^3 + 969/84155390*r^2 - 57/294543865*r + 19/17672631900 G(19,2,2,r)= r^19 - 380/39*r^18 + 570/13*r^17 - 58140/481*r^16 + 109820/481*r^15 - 1054272/3367*r^14 + 155040/481*r^13 - 103360/407*r^12 + 62985/407*r^11 - 83980/1147*r^10 + 92378/3441*r^9 - 251940/33263*r^8 + 377910/232841*r^7 - 25840/99789*r^6 + 12920/432419*r^5 - 5168/2162095*r^4 + 323/2594514*r^3 - 38/9945637*r^2 + 19/328206021*r - 2/6892326441 G(20,2,2,r)= r^20 - 420/41*r^19 + 1995/41*r^18 - 75810/533*r^17 + 305235/1066*r^16 - 8302392/19721*r^15 + 9224880/19721*r^14 - 7907040/19721*r^13 + 406980/1517*r^12 - 2351440/16687*r^11 + 88179/1517*r^10 - 881790/47027*r^9 + 440895/94054*r^8 - 1220940/1363783*r^7 + 174420/1363783*r^6 - 18088/1363783*r^5 + 33915/35458358*r^4 - 798/17729179*r^3 + 133/106375074*r^2 - 7/407771117*r + 7/89709645740 G(21,2,2,r)= r^21 - 462/43*r^20 + 2310/43*r^19 - 292600/1763*r^18 + 1250865/3526*r^17 - 12758823/22919*r^16 + 15221052/22919*r^15 - 521864640/848003*r^14 + 380526300/848003*r^13 - 16912280/65231*r^12 + 7759752/65231*r^11 - 2821728/65231*r^10 + 1616615/130462*r^9 - 5595975/2022161*r^8 + 959310/2022161*r^7 - 3581424/58642669*r^6 + 671517/117285338*r^5 - 21945/58642669*r^4 + 36575/2287064091*r^3 - 308/762354697*r^2 + 77/15247093940*r - 11/526024740930 G(22,2,2,r)= r^22 - 506/45*r^21 + 1771/30*r^20 - 24794/129*r^19 + 168245/387*r^18 - 1278662/1763*r^17 + 32605881/35260*r^16 - 105580948/114595*r^15 + 16670676/22919*r^14 - 388982440/848003*r^13 + 136143854/587079*r^12 - 91941304/978465*r^11 + 29745716/978465*r^10 - 4576264/587079*r^9 + 408595/260924*r^8 - 490314/2022161*r^7 + 572033/20221610*r^6 - 706629/293213345*r^5 + 33649/234570676*r^4 - 8855/1583352063*r^3 + 1771/13722384546*r^2 - 253/171529806825*r + 23/4116715363800 G(23,2,2,r)= r^23 - 552/47*r^22 + 3036/47*r^21 - 155848/705*r^20 + 24794/47*r^19 - 1884344/2021*r^18 + 2557324/2021*r^17 - 111791592/82861*r^16 + 475114266/414305*r^15 - 844647584/1077193*r^14 + 466778928/1077193*r^13 - 594082272/3065857*r^12 + 643589128/9197571*r^11 - 311185952/15329285*r^10 + 14382544/3065857*r^9 - 2615008/3065857*r^8 + 735471/6131714*r^7 - 1211364/95041567*r^6 + 471086/475207835*r^5 - 148764/2756205443*r^4 + 5313/2756205443*r^3 - 1012/24805848987*r^2 + 46/107492012277*r - 4/2687300306925 G(24,2,2,r)= r^24 - 600/49*r^23 + 3450/49*r^22 - 581900/2303*r^21 + 208725/329*r^20 - 55660/47*r^19 + 240350/141*r^18 - 27399900/14147*r^17 + 349348725/198058*r^16 - 5279047400/4060189*r^15 + 3167428440/4060189*r^14 - 2879480400/7540351*r^13 + 12629300/82861*r^12 - 151551600/3065857*r^11 + 277844600/21460999*r^10 - 1222516240/450680979*r^9 + 67418175/150226993*r^8 - 8652600/150226993*r^7 + 120175/21460999*r^6 - 37950/95041567*r^5 + 3795/190083134*r^4 - 12650/19293438101*r^3 + 1725/135054066707*r^2 - 50/405162200121*r + 25/63205303218876 G(25,2,2,r)= r^25 - 650/51*r^24 + 1300/17*r^23 - 239200/833*r^22 + 1891175/2499*r^21 - 8321170/5593*r^20 + 1808950/799*r^19 - 137480200/50337*r^18 + 29683225/11186*r^17 - 29683225/14147*r^16 + 403691860/297087*r^15 - 2935940800/4060189*r^14 + 183496300/580027*r^13 - 28230200/248583*r^12 + 19315400/580027*r^11 - 169975520/21460999*r^10 + 292145425/193148991*r^9 - 34370050/150226993*r^8 + 68740100/2553858881*r^7 - 2631200/1094510949*r^6 + 16445/104239138*r^5 - 82225/11309946473*r^4 + 7475/33929839419*r^3 - 1300/327988447717*r^2 + 325/9183676536076*r - 13/123979633237026 G(26,2,2,r)= r^26 - 702/53*r^25 + 8775/106*r^24 - 292500/901*r^23 + 807300/901*r^22 - 81698760/44149*r^21 + 37445265/12614*r^20 - 1123357950/296429*r^19 + 2319978375/592858*r^18 - 979546425/296429*r^17 + 160289415/69748*r^16 - 990880020/749791*r^15 + 3302933400/5248537*r^14 - 7622154000/30741431*r^13 + 2477200050/30741431*r^12 - 660586680/30741431*r^11 + 143416845/30741431*r^10 - 927991350/1137432947*r^9 + 257775375/2274865894*r^8 - 97683300/7962030629*r^7 + 19536660/19336360099*r^6 - 1184040/19336360099*r^5 + 201825/77345440396*r^4 - 43875/599427163069*r^3 + 2925/2397708652276*r^2 - 351/34766775458002*r + 27/973469712824056 G(27,2,2,r)= r^27 - 756/55*r^26 + 4914/55*r^25 - 212940/583*r^24 + 614250/583*r^23 - 22604400/9911*r^22 + 3466008/901*r^21 - 32679504/6307*r^20 + 10212345/1802*r^19 - 215593950/42347*r^18 + 160289415/42347*r^17 - 5828706/2491*r^16 + 33029334/27401*r^15 - 609772320/1178243*r^14 + 1524430800/8247701*r^13 - 2642346720/48307963*r^12 + 644072013/48307963*r^11 - 11657412/4391633*r^10 + 1874730/4391633*r^9 - 8880300/162490421*r^8 + 888030/162490421*r^7 - 473616/1137432947*r^6 + 64584/2762337157*r^5 - 28080/30385708727*r^4 + 2925/121542834908*r^3 - 351/941956970537*r^2 + 27/9419569705370*r - 1/136583760727865 G(28,2,2,r)= r^28 - 812/57*r^27 + 1827/19*r^26 - 427518/1045*r^25 + 514605/418*r^24 - 30876300/11077*r^23 + 54627300/11077*r^22 - 119659800/17119*r^21 + 138207069/17119*r^20 - 131625780/17119*r^19 + 10968815/1802*r^18 - 170515215/42347*r^17 + 22241115/9964*r^16 - 2585292/2491*r^15 + 77558760/191807*r^14 - 155117520/1178243*r^13 + 42010995/1178243*r^12 - 385512660/48307963*r^11 + 6425211/4391633*r^10 - 953810/4391633*r^9 + 4292145/166882054*r^8 - 51505740/21611225993*r^7 + 520260/3087317999*r^6 - 27144/3087317999*r^5 + 16965/52484405983*r^4 - 4524/577328465813*r^3 + 261/2309313863252*r^2 - 29/35794364880406*r + 29/15033633249770520 G(29,2,2,r)= r^29 - 870/59*r^28 + 6090/59*r^27 - 511560/1121*r^26 + 3206385/2242*r^25 - 41683005/12331*r^24 + 77190750/12331*r^23 - 6087042000/653543*r^22 + 673086375/59413*r^21 - 11517255750/1010021*r^20 + 9674494830/1010021*r^19 - 358979400/53159*r^18 + 852576075/212636*r^17 - 590244975/293938*r^16 + 872536050/1028783*r^15 - 310235040/1028783*r^14 + 145422675/1616659*r^13 - 1556878050/69516337*r^12 + 321260550/69516337*r^11 - 202901400/259106347*r^10 + 55797885/518212694*r^9 - 21460725/1813744429*r^8 + 35117550/34461144151*r^7 - 12214800/182151761941*r^6 + 593775/182151761941*r^5 - 20358/182151761941*r^4 + 7830/3096579952997*r^3 - 1160/34062379482967*r^2 + 435/1907493251046152*r - 15/29566145391215356 G(30,2,2,r)= r^30 - 930/61*r^29 + 13485/122*r^28 - 1824970/3599*r^27 + 5946885/3599*r^26 - 278314218/68381*r^25 + 2153621925/273524*r^24 - 9229808250/752191*r^23 + 11793643875/752191*r^22 - 60278624250/3624193*r^21 + 107110478475/7248386*r^20 - 681612135750/61611281*r^19 + 22720404525/3242699*r^18 - 12198396150/3242699*r^17 + 18297594225/10681832*r^16 - 41474546910/62755763*r^15 + 13524308775/62755763*r^14 - 530365050/8965109*r^13 + 2681289975/197232398*r^12 - 11007400950/4240496557*r^11 + 157248585/385499687*r^10 - 5765781450/110638410169*r^9 + 2358728775/442553640676*r^8 - 47332350/110638410169*r^7 + 7888725/300304256173*r^6 - 13253058/11111257478401*r^5 + 849555/22222514956802*r^4 - 8990/11111257478401*r^3 + 13485/1322239639929719*r^2 - 930/14544636039226909*r + 31/232714176627630544 Jacobi Polynomials G(n,4,4,r) in terms of powers: G(0,4,4,r)= 1 G(1,4,4,r)= r - 4/5 G(2,4,4,r)= r^2 - 10/7*r + 10/21 G(3,4,4,r)= r^3 - 2*r^2 + 5/4*r - 5/21 G(4,4,4,r)= r^4 - 28/11*r^3 + 126/55*r^2 - 28/33*r + 7/66 G(5,4,4,r)= r^5 - 40/13*r^4 + 140/39*r^3 - 280/143*r^2 + 70/143*r - 56/1287 G(6,4,4,r)= r^6 - 18/5*r^5 + 36/7*r^4 - 48/13*r^3 + 18/13*r^2 - 36/143*r + 12/715 G(7,4,4,r)= r^7 - 70/17*r^6 + 945/136*r^5 - 105/17*r^4 + 105/34*r^3 - 189/221*r^2 + 105/884*r - 15/2431 G(8,4,4,r)= r^8 - 88/19*r^7 + 1540/171*r^6 - 3080/323*r^5 + 1925/323*r^4 - 2156/969*r^3 + 154/323*r^2 - 220/4199*r + 55/25194 G(9,4,4,r)= r^9 - 36/7*r^8 + 396/35*r^7 - 264/19*r^6 + 198/19*r^5 - 1584/323*r^4 + 462/323*r^3 - 396/1615*r^2 + 99/4522*r - 22/29393 G(10,4,4,r)= r^10 - 130/23*r^9 + 3510/253*r^8 - 3120/161*r^7 + 390/23*r^6 - 4212/437*r^5 + 1560/437*r^4 - 6240/7429*r^3 + 1755/14858*r^2 - 65/7429*r + 13/52003 G(11,4,4,r)= r^11 - 154/25*r^10 + 1001/60*r^9 - 3003/115*r^8 + 3003/115*r^7 - 2002/115*r^6 + 9009/1150*r^5 - 5148/2185*r^4 + 1001/2185*r^3 - 2002/37145*r^2 + 1001/297160*r - 91/1114350 G(12,4,4,r)= r^12 - 20/3*r^11 + 770/39*r^10 - 308/9*r^9 + 77/2*r^8 - 3388/115*r^7 + 1078/69*r^6 - 132/23*r^5 + 33/23*r^4 - 308/1311*r^3 + 154/6555*r^2 - 28/22287*r + 7/267444 G(13,4,4,r)= r^13 - 208/29*r^12 + 4680/203*r^11 - 11440/261*r^10 + 14300/261*r^9 - 6864/145*r^8 + 12584/435*r^7 - 25168/2001*r^6 + 2574/667*r^5 - 11440/14007*r^4 + 1144/10005*r^3 - 624/63365*r^2 + 52/114057*r - 16/1938969 G(14,4,4,r)= r^14 - 238/31*r^13 + 12376/465*r^12 - 49504/899*r^11 + 68068/899*r^10 - 1769768/24273*r^9 + 136136/2697*r^8 - 1711424/67425*r^7 + 374374/40455*r^6 - 748748/310155*r^5 + 136136/310155*r^4 - 49504/930465*r^3 + 6188/1550775*r^2 - 952/5892945*r + 136/53036505 G(15,4,4,r)= r^15 - 90/11*r^14 + 5355/176*r^13 - 23205/341*r^12 + 69615/682*r^11 - 97461/899*r^10 + 301665/3596*r^9 - 43095/899*r^8 + 36465/1798*r^7 - 17017/2697*r^6 + 51051/35960*r^5 - 4641/20677*r^4 + 10829/454894*r^3 - 357/227447*r^2 + 51/909788*r - 17/21607465 G(16,4,4,r)= r^16 - 304/35*r^15 + 4104/119*r^14 - 912/11*r^13 + 1482/11*r^12 - 53352/341*r^11 + 20748/155*r^10 - 77064/899*r^9 + 260091/6293*r^8 - 282568/18879*r^7 + 10868/2697*r^6 - 17784/22475*r^5 + 494/4495*r^4 - 1064/103385*r^3 + 684/1137235*r^2 - 152/7960645*r + 19/79606450 G(17,4,4,r)= r^17 - 340/37*r^16 + 12920/333*r^15 - 25840/259*r^14 + 6460/37*r^13 - 268736/1221*r^12 + 83980/407*r^11 - 167960/1147*r^10 + 272935/3441*r^9 - 1091740/33263*r^8 + 2401828/232841*r^7 - 2183480/898101*r^6 + 41990/99789*r^5 - 5168/99789*r^4 + 1292/299367*r^3 - 2584/11475735*r^2 + 323/50493234*r - 38/530178957 G(18,4,4,r)= r^18 - 126/13*r^17 + 10710/247*r^16 - 57120/481*r^15 + 107100/481*r^14 - 145656/481*r^13 + 11424/37*r^12 - 97920/407*r^11 + 5355/37*r^10 - 77350/1147*r^9 + 27846/1147*r^8 - 222768/33263*r^7 + 46410/33263*r^6 - 7140/33263*r^5 + 10200/432419*r^4 - 3808/2162095*r^3 + 357/4324190*r^2 - 21/9945637*r + 7/328206021 G(19,4,4,r)= r^19 - 418/41*r^18 + 39501/820*r^17 - 74613/533*r^16 + 149226/533*r^15 - 8058204/19721*r^14 + 8878947/19721*r^13 - 2899248/7585*r^12 + 383724/1517*r^11 - 198968/1517*r^10 + 323323/6068*r^9 - 793611/47027*r^8 + 969969/235135*r^7 - 1044582/1363783*r^6 + 287793/2727566*r^5 - 14212/1363783*r^4 + 24871/35458358*r^3 - 13167/443229475*r^2 + 1463/2127501480*r - 77/12233133510 G(20,4,4,r)= r^20 - 460/43*r^19 + 48070/903*r^18 - 288420/1763*r^17 + 1225785/3526*r^16 - 12421288/22919*r^15 + 14709420/22919*r^14 - 500120280/848003*r^13 + 27784460/65231*r^12 - 111137840/456617*r^11 + 7191272/65231*r^10 - 7726160/195693*r^9 + 1448655/130462*r^8 - 4903140/2022161*r^7 + 817190/2022161*r^6 - 2941884/58642669*r^5 + 3677355/820997366*r^4 - 48070/175928007*r^3 + 24035/2287064091*r^2 - 506/2287064091*r + 253/137223845460 G(21,4,4,r)= r^21 - 56/5*r^20 + 644/11*r^19 - 24472/129*r^18 + 18354/43*r^17 - 1248072/1763*r^16 + 7904456/8815*r^15 - 20325744/22919*r^14 + 15912918/22919*r^13 - 28289632/65231*r^12 + 14144816/65231*r^11 - 28289632/326155*r^10 + 5408312/195693*r^9 - 4992288/717541*r^8 + 89148/65231*r^7 - 416024/2022161*r^6 + 468027/20221610*r^5 - 110124/58642669*r^4 + 6118/58642669*r^3 - 644/175928007*r^2 + 161/2287064091*r - 92/171529806825 G(22,4,4,r)= r^22 - 550/47*r^21 + 69300/1081*r^20 - 30800/141*r^19 + 73150/141*r^18 - 1843380/2021*r^17 + 2487100/2021*r^16 - 108011200/82861*r^15 + 91134450/82861*r^14 - 803333300/1077193*r^13 + 33824560/82861*r^12 - 553492800/3065857*r^11 + 591929800/9197571*r^10 - 169122800/9197571*r^9 + 12790800/3065857*r^8 - 2273920/3065857*r^7 + 621775/6131714*r^6 - 987525/95041567*r^5 + 73150/95041567*r^4 - 107800/2756205443*r^3 + 3465/2756205443*r^2 - 550/24805848987*r + 50/322476036831 G(23,4,4,r)= r^23 - 598/49*r^22 + 82225/1176*r^21 - 82225/329*r^20 + 411125/658*r^19 - 3437005/2961*r^18 + 312455/188*r^17 - 26558675/14147*r^16 + 504614825/297087*r^15 - 5046148250/4060189*r^14 + 1715690405/2320108*r^13 - 623887420/1740081*r^12 + 82090450/580027*r^11 - 138922300/3065857*r^10 + 2257487375/193148991*r^9 - 361197980/150226993*r^8 + 58429085/150226993*r^7 - 3124550/64382997*r^6 + 1562275/343375984*r^5 - 411125/1330581938*r^4 + 16445/1140498804*r^3 - 16445/38586876202*r^2 + 7475/1080432533656*r - 325/7292919602178 G(24,4,4,r)= r^24 - 216/17*r^23 + 32292/425*r^22 - 236808/833*r^21 + 88803/119*r^20 - 8169876/5593*r^19 + 12373218/5593*r^18 - 74239308/27965*r^17 + 1687257/658*r^16 - 28495896/14147*r^15 + 128231532/99029*r^14 - 396352008/580027*r^13 + 858762684/2900135*r^12 - 60977232/580027*r^11 + 17651304/580027*r^10 - 152977968/21460999*r^9 + 28683369/21460999*r^8 - 148478616/751134965*r^7 + 8248812/364836983*r^6 - 710424/364836983*r^5 + 88803/729673966*r^4 - 59202/11309946473*r^3 + 8073/56549732365*r^2 - 702/327988447717*r + 117/9183676536076 G(25,4,4,r)= r^25 - 700/53*r^24 + 56700/689*r^23 - 289800/901*r^22 + 796950/901*r^21 - 1639440/901*r^20 + 2618550/901*r^19 - 1094553900/296429*r^18 + 321227775/84694*r^17 - 7931550/2491*r^16 + 5479980/2491*r^15 - 134508600/107113*r^14 + 63517950/107113*r^13 - 1016287200/4391633*r^12 + 2286646200/30741431*r^11 - 1117915920/57091229*r^10 + 18386775/4391633*r^9 - 116810100/162490421*r^8 + 15863100/162490421*r^7 - 1669800/162490421*r^6 + 2254230/2762337157*r^5 - 910800/19336360099*r^4 + 5175/2762337157*r^3 - 4050/85632451867*r^2 + 225/342529807468*r - 9/2483341104143 G(26,4,4,r)= r^26 - 754/55*r^25 + 26390/297*r^24 - 211120/583*r^23 + 606970/583*r^22 - 6069700/2703*r^21 + 3399032/901*r^20 - 31909280/6307*r^19 + 208407485/37842*r^18 - 208407485/42347*r^17 + 9061195/2491*r^16 - 50083696/22419*r^15 + 31302310/27401*r^14 - 573073060/1178243*r^13 + 4257114160/24743103*r^12 - 17028456640/338155741*r^11 + 53213927/4391633*r^10 - 31302310/13174899*r^9 + 1647490/4391633*r^8 - 7630480/162490421*r^7 + 6676670/1462413789*r^6 - 381524/1137432947*r^5 + 346840/19336360099*r^4 - 60320/91157126181*r^3 + 1885/121542834908*r^2 - 377/1883913941074*r + 29/28258709116110 G(27,4,4,r)= r^27 - 270/19*r^26 + 50895/532*r^25 - 84825/209*r^24 + 254475/209*r^23 - 30435210/11077*r^22 + 9754875/2014*r^21 - 117058500/17119*r^20 + 134617275/17119*r^19 - 329064450/44149*r^18 + 296158005/50456*r^17 - 134617275/34874*r^16 + 37068525/17437*r^15 - 17108550/17437*r^14 + 145422675/383614*r^13 - 1008263880/8247701*r^12 + 1890494775/57733907*r^11 - 222411150/30741431*r^10 + 160630275/122965724*r^9 - 5852925/30741431*r^8 + 12876435/584087189*r^7 - 42921450/21611225993*r^6 + 5852925/43222451986*r^5 - 1017900/151278581951*r^4 + 84825/367390841881*r^3 - 20358/4041299260691*r^2 + 3915/64660788171056*r - 145/501121108325684 G(28,4,4,r)= r^28 - 868/59*r^27 + 175770/1711*r^26 - 507780/1121*r^25 + 3173625/2242*r^24 - 41130180/12331*r^23 + 75913110/12331*r^22 - 542236500/59413*r^21 + 656940375/59413*r^20 - 11192317500/1010021*r^19 + 492461970/53159*r^18 - 345362940/53159*r^17 + 47967075/12508*r^16 - 280422900/146969*r^15 + 822980250/1028783*r^14 - 41453820/146969*r^13 + 134724915/1616659*r^12 - 1426499100/69516337*r^11 + 26416650/6319667*r^10 - 180745500/259106347*r^9 + 48801285/518212694*r^8 - 18352620/1813744429*r^7 + 4171050/4923020593*r^6 - 9792900/182151761941*r^5 + 453375/182151761941*r^4 - 14508/182151761941*r^3 + 5022/3096579952997*r^2 - 620/34062379482967*r + 155/1907493251046152 G(29,4,4,r)= r^29 - 928/61*r^28 + 100688/915*r^27 - 1812384/3599*r^26 + 5890248/3599*r^25 - 274878240/68381*r^24 + 530122320/68381*r^23 - 9057518496/752191*r^22 + 1048323900/68381*r^21 - 58706138400/3624193*r^20 + 51932353200/3624193*r^19 - 34621568800/3242699*r^18 + 21811588344/3242699*r^17 - 684822240/190747*r^16 + 2168603760/1335229*r^15 - 39034867680/62755763*r^14 + 1803241170/8965109*r^13 - 490293024/8965109*r^12 + 1225732560/98616199*r^11 - 903171360/385499687*r^10 + 139776520/385499687*r^9 - 5031954720/110638410169*r^8 + 503195472/110638410169*r^7 - 5609760/15805487167*r^6 + 6310980/300304256173*r^5 - 10097568/11111257478401*r^4 + 302064/11111257478401*r^3 - 28768/55556287392005*r^2 + 7192/1322239639929719*r - 992/43633908117680727 G(30,4,4,r)= r^30 - 110/7*r^29 + 25520/217*r^28 - 102080/183*r^27 + 114840/61*r^26 - 17317872/3599*r^25 + 34834800/3599*r^24 - 1074902400/68381*r^23 + 10043619300/478667*r^22 - 11159577000/478667*r^21 + 1487943600/68381*r^20 - 62223096000/3624193*r^19 + 2193763000/190747*r^18 - 21262626000/3242699*r^17 + 607503600/190747*r^16 - 12312072960/9346603*r^15 + 4328463150/9346603*r^14 - 8656926300/62755763*r^13 + 2174686800/62755763*r^12 - 457828800/62755763*r^11 + 11445720/8965109*r^10 - 495981200/2698497809*r^9 + 405802800/18889484663*r^8 - 1552636800/774468871183*r^7 + 16173300/110638410169*r^6 - 895752/110638410169*r^5 + 689040/2102129793211*r^4 - 102080/11111257478401*r^3 + 12760/77778802348807*r^2 - 880/544451616441649*r + 176/27767032438524099 Jacobi Polynomials G(n,6,6,r) in terms of powers: G(0,6,6,r)= 1 G(1,6,6,r)= r - 6/7 G(2,6,6,r)= r^2 - 14/9*r + 7/12 G(3,6,6,r)= r^3 - 24/11*r^2 + 84/55*r - 56/165 G(4,6,6,r)= r^4 - 36/13*r^3 + 36/13*r^2 - 168/143*r + 126/715 G(5,6,6,r)= r^5 - 10/3*r^4 + 30/7*r^3 - 240/91*r^2 + 10/13*r - 12/143 G(6,6,6,r)= r^6 - 66/17*r^5 + 825/136*r^4 - 165/34*r^3 + 495/238*r^2 - 99/221*r + 33/884 G(7,6,6,r)= r^7 - 84/19*r^6 + 154/19*r^5 - 7700/969*r^4 + 5775/1292*r^3 - 462/323*r^2 + 77/323*r - 66/4199 G(8,6,6,r)= r^8 - 104/21*r^7 + 52/5*r^6 - 1144/95*r^5 + 1430/171*r^4 - 1144/323*r^3 + 286/323*r^2 - 572/4845*r + 143/22610 G(9,6,6,r)= r^9 - 126/23*r^8 + 3276/253*r^7 - 4368/253*r^6 + 1638/115*r^5 - 3276/437*r^4 + 1092/437*r^3 - 3744/7429*r^2 + 819/14858*r - 91/37145 G(10,6,6,r)= r^10 - 6*r^9 + 63/4*r^8 - 546/23*r^7 + 5733/253*r^6 - 1638/115*r^5 + 273/46*r^4 - 702/437*r^3 + 117/437*r^2 - 182/7429*r + 273/297160 G(11,6,6,r)= r^11 - 176/27*r^10 + 2200/117*r^9 - 1232/39*r^8 + 308/9*r^7 - 8624/345*r^6 + 4312/345*r^5 - 880/207*r^4 + 22/23*r^3 - 176/1311*r^2 + 616/58995*r - 112/334305 G(12,6,6,r)= r^12 - 204/29*r^11 + 4488/203*r^10 - 74800/1827*r^9 + 18700/377*r^8 - 5984/145*r^7 + 10472/435*r^6 - 32912/3335*r^5 + 1870/667*r^4 - 7480/14007*r^3 + 1496/23345*r^2 - 272/63365*r + 68/570285 G(13,6,6,r)= r^13 - 234/31*r^12 + 3978/155*r^11 - 233376/4495*r^10 + 437580/6293*r^9 - 58344/899*r^8 + 38896/899*r^7 - 466752/22475*r^6 + 160446/22475*r^5 - 106964/62031*r^4 + 29172/103385*r^3 - 21216/723695*r^2 + 884/516925*r - 408/9821575 G(14,6,6,r)= r^14 - 266/33*r^13 + 5187/176*r^12 - 88179/1364*r^11 + 29393/310*r^10 - 88179/899*r^9 + 264537/3596*r^8 - 109174/2697*r^7 + 29393/1798*r^6 - 323323/67425*r^5 + 323323/323640*r^4 - 29393/206770*r^3 + 29393/2274470*r^2 - 2261/3411705*r + 323/22744700 G(15,6,6,r)= r^15 - 60/7*r^14 + 570/17*r^13 - 14820/187*r^12 + 11115/88*r^11 - 4446/31*r^10 + 3705/31*r^9 - 66690/899*r^8 + 433485/12586*r^7 - 32110/2697*r^6 + 2717/899*r^5 - 494/899*r^4 + 247/3596*r^3 - 114/20677*r^2 + 57/227447*r - 38/7960645 G(16,6,6,r)= r^16 - 336/37*r^15 + 1400/37*r^14 - 10640/111*r^13 + 103740/629*r^12 - 82992/407*r^11 + 6916/37*r^10 - 148200/1147*r^9 + 77805/1147*r^8 - 899080/33263*r^7 + 269724/33263*r^6 - 179816/99789*r^5 + 86450/299367*r^4 - 1064/33263*r^3 + 76/33263*r^2 - 1064/11475735*r + 133/84155390 G(17,6,6,r)= r^17 - 374/39*r^16 + 10472/247*r^15 - 1047200/9139*r^14 + 916300/4329*r^13 - 10472/37*r^12 + 10472/37*r^11 - 23936/111*r^10 + 4675/37*r^9 - 65450/1147*r^8 + 68068/3441*r^7 - 173264/33263*r^6 + 34034/33263*r^5 - 130900/898101*r^4 + 18700/1297257*r^3 - 5984/6486285*r^2 + 1309/38917710*r - 77/149184555 G(18,6,6,r)= r^18 - 414/41*r^17 + 38709/820*r^16 - 361284/2665*r^15 + 2709630/10127*r^14 - 7586964/19721*r^13 + 632247/1517*r^12 - 2632212/7585*r^11 + 1703196/7585*r^10 - 172040/1517*r^9 + 270963/6068*r^8 - 640458/47027*r^7 + 747201/235135*r^6 - 3793482/6818915*r^5 + 193545/2727566*r^4 - 8602/1363783*r^3 + 12903/35458358*r^2 - 5313/443229475*r + 1771/10637507400 G(19,6,6,r)= r^19 - 456/43*r^18 + 15732/301*r^17 - 1961256/12341*r^16 + 2941884/8815*r^15 - 11767536/22919*r^14 + 13728792/22919*r^13 - 35302608/65231*r^12 + 25006014/65231*r^11 - 489006496/2283085*r^10 + 43147632/456617*r^9 - 2139552/65231*r^8 + 579462/65231*r^7 - 3744216/2022161*r^6 + 2941884/10110805*r^5 - 1961256/58642669*r^4 + 2206413/820997366*r^3 - 57684/410498683*r^2 + 9614/2287064091*r - 1012/19058867425 G(20,6,6,r)= r^20 - 100/9*r^19 + 1900/33*r^18 - 87400/473*r^17 + 371450/903*r^16 - 1188640/1763*r^15 + 1485800/1763*r^14 - 56460400/68757*r^13 + 1114350/1763*r^12 - 25258600/65231*r^11 + 111137840/587079*r^10 - 101034400/1369851*r^9 + 1485800/65231*r^8 - 11886400/2152623*r^7 + 742900/717541*r^6 - 297160/2022161*r^5 + 185725/12132966*r^4 - 65550/58642669*r^3 + 21850/410498683*r^2 - 2300/1583352063*r + 115/6861192273 G(21,6,6,r)= r^21 - 546/47*r^20 + 68250/1081*r^19 - 691600/3243*r^18 + 259350/517*r^17 - 1763580/2021*r^16 + 2351440/2021*r^15 - 100776000/82861*r^14 + 83770050/82861*r^13 - 55846700/82861*r^12 + 29980860/82861*r^11 - 479693760/3065857*r^10 + 499681000/9197571*r^9 - 46124400/3065857*r^8 + 10077600/3065857*r^7 - 18811520/33724427*r^6 + 440895/6131714*r^5 - 648375/95041567*r^4 + 43225/95041567*r^3 - 54600/2756205443*r^2 + 1365/2756205443*r - 130/24805848987 G(22,6,6,r)= r^22 - 594/49*r^21 + 3861/56*r^20 - 160875/658*r^19 + 9169875/15134*r^18 - 366795/329*r^17 + 2078505/1316*r^16 - 24942060/14147*r^15 + 155887875/99029*r^14 - 658193250/580027*r^13 + 1540172205/2320108*r^12 - 183097395/580027*r^11 + 70669170/580027*r^10 - 815413500/21460999*r^9 + 203853375/21460999*r^8 - 282676680/150226993*r^7 + 6235515/21460999*r^6 - 733590/21460999*r^5 + 1018875/343375984*r^4 - 482625/2661163876*r^3 + 19305/2661163876*r^2 - 6435/38586876202*r + 1755/1080432533656 G(23,6,6,r)= r^23 - 644/51*r^22 + 31878/425*r^21 - 118404/425*r^20 + 49335/68*r^19 - 1124838/799*r^18 + 1687257/799*r^17 - 4124406/1645*r^16 + 562419/235*r^15 - 3749460/2021*r^14 + 2374658/2021*r^13 - 50515452/82861*r^12 + 214690671/828610*r^11 - 37263864/414305*r^10 + 14709420/580027*r^9 - 17651304/3065857*r^8 + 3187041/3065857*r^7 - 2249676/15329285*r^6 + 4124406/260597845*r^5 - 65780/52119569*r^4 + 29601/416956552*r^3 - 29601/11309946473*r^2 + 897/16157066390*r - 117/234277462655 G(24,6,6,r)= r^24 - 696/53*r^23 + 56028/689*r^22 - 3697848/11713*r^21 + 19413702/22525*r^20 - 1584792/901*r^19 + 2509254/901*r^18 - 1038831156/296429*r^17 + 124208073/34874*r^16 - 36802392/12455*r^15 + 5018508/2491*r^14 - 121356648/107113*r^13 + 56344158/107113*r^12 - 884169864/4391633*r^11 + 9725868504/153707155*r^10 - 6483912336/399638603*r^9 + 191957931/57091229*r^8 - 90333144/162490421*r^7 + 11709852/162490421*r^6 - 5810904/812452105*r^5 + 1452726/2762337157*r^4 - 528264/19336360099*r^3 + 18009/19336360099*r^2 - 1566/85632451867*r + 261/1712649037340 G(25,6,6,r)= r^25 - 150/11*r^24 + 2900/33*r^23 - 1867600/5247*r^22 + 700350/689*r^21 - 1960980/901*r^20 + 3268300/901*r^19 - 30415200/6307*r^18 + 65582775/12614*r^17 - 80156725/17437*r^16 + 8364180/2491*r^15 - 5069200/2491*r^14 + 84275450/82203*r^13 - 505652700/1178243*r^12 + 1228013700/8247701*r^11 - 1309881280/30741431*r^10 + 307003425/30741431*r^9 - 108354150/57091229*r^8 + 1267300/4391633*r^7 - 5602800/162490421*r^6 + 513590/162490421*r^5 - 733700/3412298841*r^4 + 200100/19336360099*r^3 - 69600/212699961089*r^2 + 725/121542834908*r - 87/1883913941074 G(26,6,6,r)= r^26 - 806/57*r^25 + 50375/532*r^24 - 584350/1463*r^23 + 6720025/5643*r^22 - 2688010/1007*r^21 + 9408035/2014*r^20 - 336001250/51357*r^19 + 6720025/901*r^18 - 309121150/44149*r^17 + 340033265/62328*r^16 - 61824230/17437*r^15 + 33600125/17437*r^14 - 19643150/22419*r^13 + 127680475/383614*r^12 - 868227230/8247701*r^11 + 434113615/15745611*r^10 - 1276804750/215190017*r^9 + 127680475/122965724*r^8 - 13440050/92224293*r^7 + 1344005/83441027*r^6 - 29568110/21611225993*r^5 + 33600125/389002067874*r^4 - 584350/151278581951*r^3 + 292175/2571735893167*r^2 - 23374/12123897782073*r + 899/64660788171056 G(27,6,6,r)= r^27 - 864/59*r^26 + 174096/1711*r^25 - 14508000/32509*r^24 + 10881000/7847*r^23 - 40042080/12331*r^22 + 6673680/1121*r^21 - 520547040/59413*r^20 + 625657500/59413*r^19 - 556140000/53159*r^18 + 460483920/53159*r^17 - 920967840/153223*r^16 + 76747320/21889*r^15 - 1771092000/1028783*r^14 + 731538000/1028783*r^13 - 253599840/1028783*r^12 + 808349490/11316613*r^11 - 760799520/44237669*r^10 + 1056666000/309663683*r^9 - 1001052000/1813744429*r^8 + 130136760/1813744429*r^7 - 13347360/1813744429*r^6 + 20021040/34461144151*r^5 - 43524000/1275062333587*r^4 + 1813500/1275062333587*r^3 - 348192/8925436335109*r^2 + 13392/21676059670979*r - 992/238436656380769 G(28,6,6,r)= r^28 - 924/61*r^27 + 33264/305*r^26 - 8936928/17995*r^25 + 167567400/104371*r^24 - 268107840/68381*r^23 + 513873360/68381*r^22 - 792833184/68381*r^21 + 1002053052/68381*r^20 - 55669614000/3624193*r^19 + 2569366800/190747*r^18 - 32233874400/3242699*r^17 + 1181908728/190747*r^16 - 623424384/190747*r^15 + 1948201200/1335229*r^14 - 4935443040/8965109*r^13 + 1569149010/8965109*r^12 - 418439736/8965109*r^11 + 92986608/8965109*r^10 - 734104800/385499687*r^9 + 110115720/385499687*r^8 - 3817344960/110638410169*r^7 + 52054704/15805487167*r^6 - 3830112/15805487167*r^5 + 3989700/300304256173*r^4 - 5745168/11111257478401*r^3 + 147312/11111257478401*r^2 - 10912/55556287392005*r + 8184/6611198199648595 G(29,6,6,r)= r^29 - 986/63*r^28 + 10846/93*r^27 - 1041216/1891*r^26 + 563992/305*r^25 - 16919760/3599*r^24 + 33839520/3599*r^23 - 1037745280/68381*r^22 + 9631573380/478667*r^21 - 1517702472/68381*r^20 + 4215840200/205143*r^19 - 3066065600/190747*r^18 + 2034216600/190747*r^17 - 1147506800/190747*r^16 + 550803264/190747*r^15 - 11016065280/9346603*r^14 + 545065730/1335229*r^13 - 7502669460/62755763*r^12 + 1848483780/62755763*r^11 - 1141519808/188267289*r^10 + 64859080/62755763*r^9 - 389154480/2698497809*r^8 + 306606560/18889484663*r^7 - 159968640/110638410169*r^6 + 10997844/110638410169*r^5 - 563992/110638410169*r^4 + 390456/2102129793211*r^3 - 347072/77778802348807*r^2 + 43384/700009221139263*r - 2992/8166774246624735 G(30,6,6,r)= r^30 - 210/13*r^29 + 51765/416*r^28 - 189805/312*r^27 + 1708245/806*r^26 - 341649/61*r^25 + 2847075/244*r^24 - 70770150/3599*r^23 + 196448175/7198*r^22 - 2160929925/68381*r^21 + 16855253415/547048*r^20 - 3482490375/136762*r^19 + 128981125/7198*r^18 - 2053776375/190747*r^17 + 54865168875/9918844*r^16 - 6024410700/2479711*r^15 + 4518308025/4959422*r^14 - 721410525/2479711*r^13 + 240470175/3051952*r^12 - 645472575/35860436*r^11 + 61740855/17930218*r^10 - 34300475/62755763*r^9 + 2551275/35860436*r^8 - 2884050/385499687*r^7 + 480675/770999374*r^6 - 634491/15805487167*r^5 + 244035/126443897336*r^4 - 27115/410942666342*r^3 + 81345/54655374623486*r^2 - 2805/144446347219213*r + 187/1733356166630556 Powers r^n in terms of Jacobi Polynomials G(n,2,2,r): r^0 = +1*G(0,2,2,r) r^1 = +2/3*G(0,2,2,r) +1*G(1,2,2,r) r^2 = +1/2*G(0,2,2,r) +6/5*G(1,2,2,r) +1*G(2,2,2,r) r^3 = +2/5*G(0,2,2,r) +6/5*G(1,2,2,r) +12/7*G(2,2,2,r) +1*G(3,2,2,r) r^4 = +1/3*G(0,2,2,r) +8/7*G(1,2,2,r) +15/7*G(2,2,2,r) +20/9*G(3,2,2,r) +1*G(4,2,2,r) r^5 = +2/7*G(0,2,2,r) +15/14*G(1,2,2,r) +50/21*G(2,2,2,r) +10/3*G(3,2,2,r) +30/11*G(4,2,2,r) +1*G(5,2,2,r) r^6 = +1/4*G(0,2,2,r) +1*G(1,2,2,r) +5/2*G(2,2,2,r) +140/33*G(3,2,2,r) +105/22*G(4,2,2,r) +42/13*G(5,2,2,r) +1*G(6,2,2,r) r^7 = +2/9*G(0,2,2,r) +14/15*G(1,2,2,r) +28/11*G(2,2,2,r) +490/99*G(3,2,2,r) +980/143*G(4,2,2,r) +84/13*G(5,2,2,r) +56/15*G(6,2,2,r) +1*G(7,2,2,r) r^8 = +1/5*G(0,2,2,r) +48/55*G(1,2,2,r) +28/11*G(2,2,2,r) +784/143*G(3,2,2,r) +1260/143*G(4,2,2,r) +672/65*G(5,2,2,r) +42/5*G(6,2,2,r) +72/17*G(7,2,2,r) +1*G(8,2,2,r) r^9 = +2/11*G(0,2,2,r) +9/11*G(1,2,2,r) +360/143*G(2,2,2,r) +840/143*G(3,2,2,r) +1512/143*G(4,2,2,r) +189/13*G(5,2,2,r) +252/17*G(6,2,2,r) +180/17*G(7,2,2,r) +90/19*G(8,2,2,r) +1*G(9,2,2,r) r^10 = +1/6*G(0,2,2,r) +10/13*G(1,2,2,r) +225/91*G(2,2,2,r) +80/13*G(3,2,2,r) +315/26*G(4,2,2,r) +4158/221*G(5,2,2,r) +385/17*G(6,2,2,r) +6600/323*G(7,2,2,r) +495/38*G(8,2,2,r) +110/21*G(9,2,2,r) +1*G(10,2,2,r) r^11 = +2/13*G(0,2,2,r) +66/91*G(1,2,2,r) +220/91*G(2,2,2,r) +165/26*G(3,2,2,r) +2970/221*G(4,2,2,r) +5082/221*G(5,2,2,r) +10164/323*G(6,2,2,r) +10890/323*G(7,2,2,r) +3630/133*G(8,2,2,r) +110/7*G(9,2,2,r) +132/23*G(10,2,2,r) +1*G(11,2,2,r) r^12 = +1/7*G(0,2,2,r) +24/35*G(1,2,2,r) +33/14*G(2,2,2,r) +110/17*G(3,2,2,r) +495/34*G(4,2,2,r) +8712/323*G(5,2,2,r) +66066/1615*G(6,2,2,r) +113256/2261*G(7,2,2,r) +6435/133*G(8,2,2,r) +5720/161*G(9,2,2,r) +429/23*G(10,2,2,r) +156/25*G(11,2,2,r) +1*G(12,2,2,r) r^13 = +2/15*G(0,2,2,r) +13/20*G(1,2,2,r) +39/17*G(2,2,2,r) +1001/153*G(3,2,2,r) +5005/323*G(4,2,2,r) +99099/3230*G(5,2,2,r) +81796/1615*G(6,2,2,r) +22308/323*G(7,2,2,r) +33462/437*G(8,2,2,r) +9295/138*G(9,2,2,r) +26026/575*G(10,2,2,r) +546/25*G(11,2,2,r) +182/27*G(12,2,2,r) +1*G(13,2,2,r) r^14 = +1/8*G(0,2,2,r) +21/34*G(1,2,2,r) +455/204*G(2,2,2,r) +6370/969*G(3,2,2,r) +21021/1292*G(4,2,2,r) +11011/323*G(5,2,2,r) +39039/646*G(6,2,2,r) +669240/7429*G(7,2,2,r) +195195/1748*G(8,2,2,r) +13013/115*G(9,2,2,r) +21021/230*G(10,2,2,r) +2548/45*G(11,2,2,r) +455/18*G(12,2,2,r) +210/29*G(13,2,2,r) +1*G(14,2,2,r) r^15 = +2/17*G(0,2,2,r) +10/17*G(1,2,2,r) +700/323*G(2,2,2,r) +6370/969*G(3,2,2,r) +5460/323*G(4,2,2,r) +12012/323*G(5,2,2,r) +520520/7429*G(6,2,2,r) +836550/7429*G(7,2,2,r) +66924/437*G(8,2,2,r) +4004/23*G(9,2,2,r) +56056/345*G(10,2,2,r) +364/3*G(11,2,2,r) +18200/261*G(12,2,2,r) +840/29*G(13,2,2,r) +240/31*G(14,2,2,r) +1*G(15,2,2,r) r^16 = +1/9*G(0,2,2,r) +32/57*G(1,2,2,r) +40/19*G(2,2,2,r) +1120/171*G(3,2,2,r) +3640/209*G(4,2,2,r) +17472/437*G(5,2,2,r) +104104/1311*G(6,2,2,r) +59488/437*G(7,2,2,r) +87516/437*G(8,2,2,r) +155584/621*G(9,2,2,r) +272272/1035*G(10,2,2,r) +99008/435*G(11,2,2,r) +123760/783*G(12,2,2,r) +76160/899*G(13,2,2,r) +1020/31*G(14,2,2,r) +272/33*G(15,2,2,r) +1*G(16,2,2,r) r^17 = +2/19*G(0,2,2,r) +51/95*G(1,2,2,r) +272/133*G(2,2,2,r) +1360/209*G(3,2,2,r) +85680/4807*G(4,2,2,r) +18564/437*G(5,2,2,r) +965328/10925*G(6,2,2,r) +350064/2185*G(7,2,2,r) +330616/1311*G(8,2,2,r) +165308/483*G(9,2,2,r) +1322464/3335*G(10,2,2,r) +841568/2175*G(11,2,2,r) +841568/2697*G(12,2,2,r) +182070/899*G(13,2,2,r) +34680/341*G(14,2,2,r) +408/11*G(15,2,2,r) +306/35*G(16,2,2,r) +1*G(17,2,2,r) r^18 = +1/10*G(0,2,2,r) +18/35*G(1,2,2,r) +153/77*G(2,2,2,r) +1632/253*G(3,2,2,r) +4590/253*G(4,2,2,r) +25704/575*G(5,2,2,r) +55692/575*G(6,2,2,r) +21216/115*G(7,2,2,r) +247962/805*G(8,2,2,r) +6281704/14007*G(9,2,2,r) +9422556/16675*G(10,2,2,r) +13705536/22475*G(11,2,2,r) +499681/899*G(12,2,2,r) +4151196/9889*G(13,2,2,r) +87210/341*G(14,2,2,r) +46512/385*G(15,2,2,r) +2907/70*G(16,2,2,r) +342/37*G(17,2,2,r) +1*G(18,2,2,r) r^19 = +2/21*G(0,2,2,r) +38/77*G(1,2,2,r) +3420/1771*G(2,2,2,r) +1615/253*G(3,2,2,r) +23256/1265*G(4,2,2,r) +69768/1495*G(5,2,2,r) +36176/345*G(6,2,2,r) +33592/161*G(7,2,2,r) +1713192/4669*G(8,2,2,r) +119352376/210105*G(9,2,2,r) +238704752/310155*G(10,2,2,r) +4068831/4495*G(11,2,2,r) +27125540/29667*G(12,2,2,r) +7732620/9889*G(13,2,2,r) +1325592/2387*G(14,2,2,r) +24548/77*G(15,2,2,r) +36822/259*G(16,2,2,r) +1710/37*G(17,2,2,r) +380/39*G(18,2,2,r) +1*G(19,2,2,r) r^20 = +1/11*G(0,2,2,r) +120/253*G(1,2,2,r) +475/253*G(2,2,2,r) +1596/253*G(3,2,2,r) +61047/3289*G(4,2,2,r) +72352/1495*G(5,2,2,r) +2584/23*G(6,2,2,r) +155040/667*G(7,2,2,r) +285532/667*G(8,2,2,r) +43400864/62031*G(9,2,2,r) +104433329/103385*G(10,2,2,r) +37975756/29667*G(11,2,2,r) +13961675/9889*G(12,2,2,r) +13255920/9889*G(13,2,2,r) +368220/341*G(14,2,2,r) +294576/407*G(15,2,2,r) +14535/37*G(16,2,2,r) +79800/481*G(17,2,2,r) +665/13*G(18,2,2,r) +420/41*G(19,2,2,r) +1*G(20,2,2,r) r^21 = +2/23*G(0,2,2,r) +21/46*G(1,2,2,r) +42/23*G(2,2,2,r) +1862/299*G(3,2,2,r) +5586/299*G(4,2,2,r) +74613/1495*G(5,2,2,r) +397936/3335*G(6,2,2,r) +170544/667*G(7,2,2,r) +10147368/20677*G(8,2,2,r) +104433329/124062*G(9,2,2,r) +132915146/103385*G(10,2,2,r) +7818538/4495*G(11,2,2,r) +5584670/2697*G(12,2,2,r) +1933155/899*G(13,2,2,r) +2209320/1147*G(14,2,2,r) +54264/37*G(15,2,2,r) +447678/481*G(16,2,2,r) +460845/962*G(17,2,2,r) +102410/533*G(18,2,2,r) +2310/41*G(19,2,2,r) +462/43*G(20,2,2,r) +1*G(21,2,2,r) r^22 = +1/12*G(0,2,2,r) +11/25*G(1,2,2,r) +231/130*G(2,2,2,r) +2156/351*G(3,2,2,r) +1463/78*G(4,2,2,r) +96558/1885*G(5,2,2,r) +273581/2175*G(6,2,2,r) +1250656/4495*G(7,2,2,r) +1993233/3596*G(8,2,2,r) +8033333/8091*G(9,2,2,r) +43001959/26970*G(10,2,2,r) +51378964/22475*G(11,2,2,r) +141292151/48546*G(12,2,2,r) +108686270/33263*G(13,2,2,r) +3677355/1147*G(14,2,2,r) +1307504/481*G(15,2,2,r) +18877089/9620*G(16,2,2,r) +23318757/19721*G(17,2,2,r) +1850695/3198*G(18,2,2,r) +389620/1763*G(19,2,2,r) +5313/86*G(20,2,2,r) +506/45*G(21,2,2,r) +1*G(22,2,2,r) r^23 = +2/25*G(0,2,2,r) +138/325*G(1,2,2,r) +1012/585*G(2,2,2,r) +3542/585*G(3,2,2,r) +7084/377*G(4,2,2,r) +1480556/28275*G(5,2,2,r) +2961112/22475*G(6,2,2,r) +2696727/8990*G(7,2,2,r) +2778446/4495*G(8,2,2,r) +3105322/2697*G(9,2,2,r) +43474508/22475*G(10,2,2,r) +590858086/202275*G(11,2,2,r) +1181716172/299367*G(12,2,2,r) +157881108/33263*G(13,2,2,r) +75181480/14911*G(14,2,2,r) +11277222/2405*G(15,2,2,r) +372148326/98605*G(16,2,2,r) +51079182/19721*G(17,2,2,r) +34052788/22919*G(18,2,2,r) +1221990/1763*G(19,2,2,r) +162932/645*G(20,2,2,r) +1012/15*G(21,2,2,r) +552/47*G(22,2,2,r) +1*G(23,2,2,r) r^24 = +1/13*G(0,2,2,r) +16/39*G(1,2,2,r) +460/273*G(2,2,2,r) +20240/3393*G(3,2,2,r) +7084/377*G(4,2,2,r) +623392/11687*G(5,2,2,r) +370139/2697*G(6,2,2,r) +288420/899*G(7,2,2,r) +1225785/1798*G(8,2,2,r) +24842576/18879*G(9,2,2,r) +6210644/2697*G(10,2,2,r) +363604976/99789*G(11,2,2,r) +1554889700/299367*G(12,2,2,r) +2870565600/432419*G(13,2,2,r) +112772220/14911*G(14,2,2,r) +150362960/19721*G(15,2,2,r) +930370815/138047*G(16,2,2,r) +4378215600/848003*G(17,2,2,r) +77392700/22919*G(18,2,2,r) +3258640/1763*G(19,2,2,r) +35420/43*G(20,2,2,r) +40480/141*G(21,2,2,r) +3450/47*G(22,2,2,r) +600/49*G(23,2,2,r) +1*G(24,2,2,r) r^25 = +2/27*G(0,2,2,r) +25/63*G(1,2,2,r) +1000/609*G(2,2,2,r) +4600/783*G(3,2,2,r) +50600/2697*G(4,2,2,r) +97405/1798*G(5,2,2,r) +1151150/8091*G(6,2,2,r) +15622750/45849*G(7,2,2,r) +4686825/6293*G(8,2,2,r) +504614825/339822*G(9,2,2,r) +807383720/299367*G(10,2,2,r) +444254200/99789*G(11,2,2,r) +5980345000/898101*G(12,2,2,r) +299017250/33263*G(13,2,2,r) +512601000/47027*G(14,2,2,r) +375907400/31857*G(15,2,2,r) +5168726750/456617*G(16,2,2,r) +621905625/65231*G(17,2,2,r) +110561000/15867*G(18,2,2,r) +23023000/5289*G(19,2,2,r) +4604600/2021*G(20,2,2,r) +411125/423*G(21,2,2,r) +747500/2303*G(22,2,2,r) +3900/49*G(23,2,2,r) +650/51*G(24,2,2,r) +1*G(25,2,2,r) r^26 = +1/14*G(0,2,2,r) +78/203*G(1,2,2,r) +325/203*G(2,2,2,r) +5200/899*G(3,2,2,r) +67275/3596*G(4,2,2,r) +49335/899*G(5,2,2,r) +4489485/30566*G(6,2,2,r) +38481300/106981*G(7,2,2,r) +20309575/25172*G(8,2,2,r) +385881925/232841*G(9,2,2,r) +207157665/66526*G(10,2,2,r) +177701680/33263*G(11,2,2,r) +277658875/33263*G(12,2,2,r) +16146931500/1363783*G(13,2,2,r) +4997859750/329189*G(14,2,2,r) +7996575600/456617*G(15,2,2,r) +16492937175/913234*G(16,2,2,r) +1077969750/65231*G(17,2,2,r) +23434125/1763*G(18,2,2,r) +769626000/82861*G(19,2,2,r) +22447425/4042*G(20,2,2,r) +6413550/2303*G(21,2,2,r) +2623725/2303*G(22,2,2,r) +304200/833*G(23,2,2,r) +2925/34*G(24,2,2,r) +702/53*G(25,2,2,r) +1*G(26,2,2,r) r^27 = +2/29*G(0,2,2,r) +54/145*G(1,2,2,r) +1404/899*G(2,2,2,r) +20475/3596*G(3,2,2,r) +184275/9889*G(4,2,2,r) +847665/15283*G(5,2,2,r) +2308878/15283*G(6,2,2,r) +5772195/15283*G(7,2,2,r) +28860975/33263*G(8,2,2,r) +60928725/33263*G(9,2,2,r) +118107990/33263*G(10,2,2,r) +419820219/66526*G(11,2,2,r) +13994007300/1363783*G(12,2,2,r) +20760340500/1363783*G(13,2,2,r) +41520681000/2022161*G(14,2,2,r) +17992295100/717541*G(15,2,2,r) +1799229510/65231*G(16,2,2,r) +1771619850/65231*G(17,2,2,r) +1968466500/82861*G(18,2,2,r) +3030402375/165722*G(19,2,2,r) +173165850/14147*G(20,2,2,r) +2308878/329*G(21,2,2,r) +18890820/5593*G(22,2,2,r) +157950/119*G(23,2,2,r) +368550/901*G(24,2,2,r) +4914/53*G(25,2,2,r) +756/55*G(26,2,2,r) +1*G(27,2,2,r) r^28 = +1/15*G(0,2,2,r) +56/155*G(1,2,2,r) +189/124*G(2,2,2,r) +1911/341*G(3,2,2,r) +429975/23188*G(4,2,2,r) +29484/527*G(5,2,2,r) +81627/527*G(6,2,2,r) +7696260/19499*G(7,2,2,r) +40405365/43586*G(8,2,2,r) +2302300/1147*G(9,2,2,r) +9186177/2294*G(10,2,2,r) +345734298/47027*G(11,2,2,r) +1166167275/94054*G(12,2,2,r) +38752635600/2022161*G(13,2,2,r) +602049874500/22243771*G(14,2,2,r) +24973920720/717541*G(15,2,2,r) +2646692685/65231*G(16,2,2,r) +130777756200/3065857*G(17,2,2,r) +6659978325/165722*G(18,2,2,r) +2789894250/82861*G(19,2,2,r) +100436193/4042*G(20,2,2,r) +89276616/5593*G(21,2,2,r) +7023510/799*G(22,2,2,r) +3664440/901*G(23,2,2,r) +1385475/901*G(24,2,2,r) +1330056/2915*G(25,2,2,r) +5481/55*G(26,2,2,r) +812/57*G(27,2,2,r) +1*G(28,2,2,r) r^29 = +2/31*G(0,2,2,r) +87/248*G(1,2,2,r) +1015/682*G(2,2,2,r) +63945/11594*G(3,2,2,r) +213759/11594*G(4,2,2,r) +118755/2108*G(5,2,2,r) +3087630/19499*G(6,2,2,r) +152176050/370481*G(7,2,2,r) +21460725/21793*G(8,2,2,r) +10015005/4588*G(9,2,2,r) +210315105/47027*G(10,2,2,r) +397868835/47027*G(11,2,2,r) +29840162625/2022161*G(12,2,2,r) +1053587280375/44487542*G(13,2,2,r) +775975393800/22243771*G(14,2,2,r) +33738060600/717541*G(15,2,2,r) +177124818150/3065857*G(16,2,2,r) +790115610375/12263428*G(17,2,2,r) +5374936125/82861*G(18,2,2,r) +4854415995/82861*G(19,2,2,r) +1618138665/34357*G(20,2,2,r) +373416615/11186*G(21,2,2,r) +6110453700/296429*G(22,2,2,r) +9839700/901*G(23,2,2,r) +48214530/9911*G(24,2,2,r) +2066337/1166*G(25,2,2,r) +105966/209*G(26,2,2,r) +2030/19*G(27,2,2,r) +870/59*G(28,2,2,r) +1*G(29,2,2,r) r^30 = +1/16*G(0,2,2,r) +15/44*G(1,2,2,r) +2175/1496*G(2,2,2,r) +1015/187*G(3,2,2,r) +27405/1496*G(4,2,2,r) +71253/1258*G(5,2,2,r) +7719075/47804*G(6,2,2,r) +5089500/11951*G(7,2,2,r) +5852925/5624*G(8,2,2,r) +7153575/3034*G(9,2,2,r) +30045015/6068*G(10,2,2,r) +628213950/65231*G(11,2,2,r) +49733604375/2870164*G(12,2,2,r) +20658574125/717541*G(13,2,2,r) +63258863625/1435082*G(14,2,2,r) +2091759757200/33724427*G(15,2,2,r) +1961024772375/24526856*G(16,2,2,r) +576771991875/6131714*G(17,2,2,r) +33324603975/331444*G(18,2,2,r) +136806268950/1408637*G(19,2,2,r) +11575915065/137428*G(20,2,2,r) +19293191775/296429*G(21,2,2,r) +26308897875/592858*G(22,2,2,r) +1830184200/69377*G(23,2,2,r) +533803725/39644*G(24,2,2,r) +64056447/11077*G(25,2,2,r) +849555/418*G(26,2,2,r) +629300/1121*G(27,2,2,r) +13485/118*G(28,2,2,r) +930/61*G(29,2,2,r) +1*G(30,2,2,r) Zernike polynomials R(n,m,r) in terms of Jacobi Polynomials G(n,2,2,r): R(0,0,r) = +1*G(0,2,2,r) R(1,1,r) = +2/3*G(0,2,2,r) +1*G(1,2,2,r) R(2,0,r) = +12/5*G(1,2,2,r) +2*G(2,2,2,r) R(2,2,r) = +1/2*G(0,2,2,r) +6/5*G(1,2,2,r) +1*G(2,2,2,r) R(3,1,r) = -2/15*G(0,2,2,r) +8/5*G(1,2,2,r) +36/7*G(2,2,2,r) +3*G(3,2,2,r) R(3,3,r) = +2/5*G(0,2,2,r) +6/5*G(1,2,2,r) +12/7*G(2,2,2,r) +1*G(3,2,2,r) R(4,0,r) = -12/35*G(1,2,2,r) +48/7*G(2,2,2,r) +40/3*G(3,2,2,r) +6*G(4,2,2,r) R(4,2,r) = -1/6*G(0,2,2,r) +34/35*G(1,2,2,r) +39/7*G(2,2,2,r) +80/9*G(3,2,2,r) +4*G(4,2,2,r) R(4,4,r) = +1/3*G(0,2,2,r) +8/7*G(1,2,2,r) +15/7*G(2,2,2,r) +20/9*G(3,2,2,r) +1*G(4,2,2,r) R(5,1,r) = +2/35*G(0,2,2,r) -24/35*G(1,2,2,r) +68/21*G(2,2,2,r) +64/3*G(3,2,2,r) +300/11*G(4,2,2,r) +10*G(5,2,2,r) R(5,3,r) = -6/35*G(0,2,2,r) +39/70*G(1,2,2,r) +106/21*G(2,2,2,r) +38/3*G(3,2,2,r) +150/11*G(4,2,2,r) +5*G(5,2,2,r) R(5,5,r) = +2/7*G(0,2,2,r) +15/14*G(1,2,2,r) +50/21*G(2,2,2,r) +10/3*G(3,2,2,r) +30/11*G(4,2,2,r) +1*G(5,2,2,r) R(6,0,r) = +4/35*G(1,2,2,r) -16/7*G(2,2,2,r) +200/11*G(3,2,2,r) +720/11*G(4,2,2,r) +840/13*G(5,2,2,r) +20*G(6,2,2,r) R(6,2,r) = +1/12*G(0,2,2,r) -23/35*G(1,2,2,r) +9/14*G(2,2,2,r) +1900/99*G(3,2,2,r) +1135/22*G(4,2,2,r) +630/13*G(5,2,2,r) +15*G(6,2,2,r) R(6,4,r) = -1/6*G(0,2,2,r) +2/7*G(1,2,2,r) +30/7*G(2,2,2,r) +1420/99*G(3,2,2,r) +260/11*G(4,2,2,r) +252/13*G(5,2,2,r) +6*G(6,2,2,r) R(6,6,r) = +1/4*G(0,2,2,r) +1*G(1,2,2,r) +5/2*G(2,2,2,r) +140/33*G(3,2,2,r) +105/22*G(4,2,2,r) +42/13*G(5,2,2,r) +1*G(6,2,2,r) R(7,1,r) = -2/63*G(0,2,2,r) +8/21*G(1,2,2,r) -180/77*G(2,2,2,r) +320/99*G(3,2,2,r) +10900/143*G(4,2,2,r) +2160/13*G(5,2,2,r) +392/3*G(6,2,2,r) +35*G(7,2,2,r) R(7,3,r) = +2/21*G(0,2,2,r) -19/35*G(1,2,2,r) -64/77*G(2,2,2,r) +460/33*G(3,2,2,r) +8880/143*G(4,2,2,r) +1374/13*G(5,2,2,r) +392/5*G(6,2,2,r) +21*G(7,2,2,r) R(7,5,r) = -10/63*G(0,2,2,r) +11/105*G(1,2,2,r) +272/77*G(2,2,2,r) +1450/99*G(3,2,2,r) +4520/143*G(4,2,2,r) +510/13*G(5,2,2,r) +392/15*G(6,2,2,r) +7*G(7,2,2,r) R(7,7,r) = +2/9*G(0,2,2,r) +14/15*G(1,2,2,r) +28/11*G(2,2,2,r) +490/99*G(3,2,2,r) +980/143*G(4,2,2,r) +84/13*G(5,2,2,r) +56/15*G(6,2,2,r) +1*G(7,2,2,r) R(8,0,r) = -4/77*G(1,2,2,r) +80/77*G(2,2,2,r) -4360/429*G(3,2,2,r) +5520/143*G(4,2,2,r) +3528/13*G(5,2,2,r) +448*G(6,2,2,r) +5040/17*G(7,2,2,r) +70*G(8,2,2,r) R(8,2,r) = -1/20*G(0,2,2,r) +171/385*G(1,2,2,r) -213/154*G(2,2,2,r) -2188/429*G(3,2,2,r) +14955/286*G(4,2,2,r) +15582/65*G(5,2,2,r) +1827/5*G(6,2,2,r) +4032/17*G(7,2,2,r) +56*G(8,2,2,r) R(8,4,r) = +1/10*G(0,2,2,r) -162/385*G(1,2,2,r) -122/77*G(2,2,2,r) +3716/429*G(3,2,2,r) +8760/143*G(4,2,2,r) +9996/65*G(5,2,2,r) +966/5*G(6,2,2,r) +2016/17*G(7,2,2,r) +28*G(8,2,2,r) R(8,6,r) = -3/20*G(0,2,2,r) -1/55*G(1,2,2,r) +63/22*G(2,2,2,r) +6076/429*G(3,2,2,r) +10605/286*G(4,2,2,r) +3906/65*G(5,2,2,r) +301/5*G(6,2,2,r) +576/17*G(7,2,2,r) +8*G(8,2,2,r) R(8,8,r) = +1/5*G(0,2,2,r) +48/55*G(1,2,2,r) +28/11*G(2,2,2,r) +784/143*G(3,2,2,r) +1260/143*G(4,2,2,r) +672/65*G(5,2,2,r) +42/5*G(6,2,2,r) +72/17*G(7,2,2,r) +1*G(8,2,2,r) R(9,1,r) = +2/99*G(0,2,2,r) -8/33*G(1,2,2,r) +1620/1001*G(2,2,2,r) -7360/1287*G(3,2,2,r) -1988/143*G(4,2,2,r) +3024/13*G(5,2,2,r) +41944/51*G(6,2,2,r) +17920/17*G(7,2,2,r) +11340/19*G(8,2,2,r) +126*G(9,2,2,r) R(9,3,r) = -2/33*G(0,2,2,r) +47/110*G(1,2,2,r) -454/1001*G(2,2,2,r) -3470/429*G(3,2,2,r) +3318/143*G(4,2,2,r) +3129/13*G(5,2,2,r) +52528/85*G(6,2,2,r) +12264/17*G(7,2,2,r) +7560/19*G(8,2,2,r) +84*G(9,2,2,r) R(9,5,r) = +10/99*G(0,2,2,r) -103/330*G(1,2,2,r) -274/143*G(2,2,2,r) +5530/1287*G(3,2,2,r) +7742/143*G(4,2,2,r) +2373/13*G(5,2,2,r) +82768/255*G(6,2,2,r) +5528/17*G(7,2,2,r) +3240/19*G(8,2,2,r) +36*G(9,2,2,r) R(9,7,r) = -14/99*G(0,2,2,r) -17/165*G(1,2,2,r) +328/143*G(2,2,2,r) +17080/1287*G(3,2,2,r) +5768/143*G(4,2,2,r) +1029/13*G(5,2,2,r) +26404/255*G(6,2,2,r) +1484/17*G(7,2,2,r) +810/19*G(8,2,2,r) +9*G(9,2,2,r) R(9,9,r) = +2/11*G(0,2,2,r) +9/11*G(1,2,2,r) +360/143*G(2,2,2,r) +840/143*G(3,2,2,r) +1512/143*G(4,2,2,r) +189/13*G(5,2,2,r) +252/17*G(6,2,2,r) +180/17*G(7,2,2,r) +90/19*G(8,2,2,r) +1*G(9,2,2,r) R(10,0,r) = +4/143*G(1,2,2,r) -80/143*G(2,2,2,r) +840/143*G(3,2,2,r) -5040/143*G(4,2,2,r) +8232/221*G(5,2,2,r) +16576/17*G(6,2,2,r) +801360/323*G(7,2,2,r) +50400/19*G(8,2,2,r) +1320*G(9,2,2,r) +252*G(10,2,2,r) R(10,2,r) = +1/30*G(0,2,2,r) -226/715*G(1,2,2,r) +189/143*G(2,2,2,r) -224/1287*G(3,2,2,r) -4585/143*G(4,2,2,r) +107604/1105*G(5,2,2,r) +80094/85*G(6,2,2,r) +696528/323*G(7,2,2,r) +42399/19*G(8,2,2,r) +1100*G(9,2,2,r) +210*G(10,2,2,r) R(10,4,r) = -1/15*G(0,2,2,r) +272/715*G(1,2,2,r) +249/1001*G(2,2,2,r) -10532/1287*G(3,2,2,r) +35/143*G(4,2,2,r) +215712/1105*G(5,2,2,r) +65352/85*G(6,2,2,r) +447264/323*G(7,2,2,r) +24912/19*G(8,2,2,r) +4400/7*G(9,2,2,r) +120*G(10,2,2,r) R(10,6,r) = +1/10*G(0,2,2,r) -158/715*G(1,2,2,r) -2011/1001*G(2,2,2,r) +32/33*G(3,2,2,r) +1155/26*G(4,2,2,r) +212982/1105*G(5,2,2,r) +37597/85*G(6,2,2,r) +198504/323*G(7,2,2,r) +19539/38*G(8,2,2,r) +1650/7*G(9,2,2,r) +45*G(10,2,2,r) R(10,8,r) = -2/15*G(0,2,2,r) -116/715*G(1,2,2,r) +1818/1001*G(2,2,2,r) +1744/143*G(3,2,2,r) +5985/143*G(4,2,2,r) +105084/1105*G(5,2,2,r) +12824/85*G(6,2,2,r) +53688/323*G(7,2,2,r) +2304/19*G(8,2,2,r) +1100/21*G(9,2,2,r) +10*G(10,2,2,r) R(10,10,r) = +1/6*G(0,2,2,r) +10/13*G(1,2,2,r) +225/91*G(2,2,2,r) +80/13*G(3,2,2,r) +315/26*G(4,2,2,r) +4158/221*G(5,2,2,r) +385/17*G(6,2,2,r) +6600/323*G(7,2,2,r) +495/38*G(8,2,2,r) +110/21*G(9,2,2,r) +1*G(10,2,2,r) R(11,1,r) = -2/143*G(0,2,2,r) +24/143*G(1,2,2,r) -500/429*G(2,2,2,r) +2240/429*G(3,2,2,r) -14700/2431*G(4,2,2,r) -24976/221*G(5,2,2,r) +182280/323*G(6,2,2,r) +1128960/323*G(7,2,2,r) +126180/19*G(8,2,2,r) +6000*G(9,2,2,r) +60984/23*G(10,2,2,r) +462*G(11,2,2,r) R(11,3,r) = +6/143*G(0,2,2,r) -1662/5005*G(1,2,2,r) +188/231*G(2,2,2,r) +1480/429*G(3,2,2,r) -71700/2431*G(4,2,2,r) -4172/221*G(5,2,2,r) +1219176/1615*G(6,2,2,r) +965088/323*G(7,2,2,r) +668700/133*G(8,2,2,r) +30420/7*G(9,2,2,r) +43560/23*G(10,2,2,r) +330*G(11,2,2,r) R(11,5,r) = -10/143*G(0,2,2,r) +1626/5005*G(1,2,2,r) +2188/3003*G(2,2,2,r) -5975/858*G(3,2,2,r) -35850/2431*G(4,2,2,r) +29330/221*G(5,2,2,r) +1286292/1615*G(6,2,2,r) +647046/323*G(7,2,2,r) +372150/133*G(8,2,2,r) +15630/7*G(9,2,2,r) +21780/23*G(10,2,2,r) +165*G(11,2,2,r) R(11,7,r) = +14/143*G(0,2,2,r) -732/5005*G(1,2,2,r) -1972/1001*G(2,2,2,r) -415/286*G(3,2,2,r) +83250/2431*G(4,2,2,r) +41748/221*G(5,2,2,r) +857556/1615*G(6,2,2,r) +302778/323*G(7,2,2,r) +142950/133*G(8,2,2,r) +5420/7*G(9,2,2,r) +7260/23*G(10,2,2,r) +55*G(11,2,2,r) R(11,9,r) = -18/143*G(0,2,2,r) -204/1001*G(1,2,2,r) +1420/1001*G(2,2,2,r) +3165/286*G(3,2,2,r) +102330/2431*G(4,2,2,r) +23772/221*G(5,2,2,r) +63924/323*G(6,2,2,r) +85590/323*G(7,2,2,r) +1770/7*G(8,2,2,r) +1140/7*G(9,2,2,r) +1452/23*G(10,2,2,r) +11*G(11,2,2,r) R(11,11,r) = +2/13*G(0,2,2,r) +66/91*G(1,2,2,r) +220/91*G(2,2,2,r) +165/26*G(3,2,2,r) +2970/221*G(4,2,2,r) +5082/221*G(5,2,2,r) +10164/323*G(6,2,2,r) +10890/323*G(7,2,2,r) +3630/133*G(8,2,2,r) +110/7*G(9,2,2,r) +132/23*G(10,2,2,r) +1*G(11,2,2,r) R(12,0,r) = -12/715*G(1,2,2,r) +48/143*G(2,2,2,r) -26600/7293*G(3,2,2,r) +62160/2431*G(4,2,2,r) -390600/4199*G(5,2,2,r) -321216/1615*G(6,2,2,r) +963792/323*G(7,2,2,r) +223200/19*G(8,2,2,r) +421080/23*G(9,2,2,r) +332640/23*G(10,2,2,r) +144144/25*G(11,2,2,r) +924*G(12,2,2,r) R(12,2,r) = -1/42*G(0,2,2,r) +1178/5005*G(1,2,2,r) -1137/1001*G(2,2,2,r) +44480/21879*G(3,2,2,r) +35515/2431*G(4,2,2,r) -37908/323*G(5,2,2,r) -12558/1615*G(6,2,2,r) +7108272/2261*G(7,2,2,r) +1429605/133*G(8,2,2,r) +2582140/161*G(9,2,2,r) +286638/23*G(10,2,2,r) +123552/25*G(11,2,2,r) +792*G(12,2,2,r) R(12,4,r) = +1/21*G(0,2,2,r) -320/1001*G(1,2,2,r) +645/2002*G(2,2,2,r) +113990/21879*G(3,2,2,r) -92605/4862*G(4,2,2,r) -360072/4199*G(5,2,2,r) +140574/323*G(6,2,2,r) +7143480/2261*G(7,2,2,r) +1066005/133*G(8,2,2,r) +1718200/161*G(9,2,2,r) +181995/23*G(10,2,2,r) +15444/5*G(11,2,2,r) +495*G(12,2,2,r) R(12,6,r) = -1/14*G(0,2,2,r) +270/1001*G(1,2,2,r) +1035/1001*G(2,2,2,r) -12840/2431*G(3,2,2,r) -112095/4862*G(4,2,2,r) +22986/323*G(5,2,2,r) +235599/323*G(6,2,2,r) +5494680/2261*G(7,2,2,r) +1211985/266*G(8,2,2,r) +840950/161*G(9,2,2,r) +82995/23*G(10,2,2,r) +6864/5*G(11,2,2,r) +220*G(12,2,2,r) R(12,8,r) = +2/21*G(0,2,2,r) -428/5005*G(1,2,2,r) -1863/1001*G(2,2,2,r) -7660/2431*G(3,2,2,r) +60030/2431*G(4,2,2,r) +738180/4199*G(5,2,2,r) +947576/1615*G(6,2,2,r) +2823816/2261*G(7,2,2,r) +240120/133*G(8,2,2,r) +854260/483*G(9,2,2,r) +25784/23*G(10,2,2,r) +10296/25*G(11,2,2,r) +66*G(12,2,2,r) R(12,10,r) = -5/42*G(0,2,2,r) -106/455*G(1,2,2,r) +99/91*G(2,2,2,r) +2200/221*G(3,2,2,r) +18315/442*G(4,2,2,r) +490050/4199*G(5,2,2,r) +390467/1615*G(6,2,2,r) +850872/2261*G(7,2,2,r) +116325/266*G(8,2,2,r) +178090/483*G(9,2,2,r) +4895/23*G(10,2,2,r) +1872/25*G(11,2,2,r) +12*G(12,2,2,r) R(12,12,r) = +1/7*G(0,2,2,r) +24/35*G(1,2,2,r) +33/14*G(2,2,2,r) +110/17*G(3,2,2,r) +495/34*G(4,2,2,r) +8712/323*G(5,2,2,r) +66066/1615*G(6,2,2,r) +113256/2261*G(7,2,2,r) +6435/133*G(8,2,2,r) +5720/161*G(9,2,2,r) +429/23*G(10,2,2,r) +156/25*G(11,2,2,r) +1*G(12,2,2,r) R(13,1,r) = +2/195*G(0,2,2,r) -8/65*G(1,2,2,r) +2124/2431*G(2,2,2,r) -31808/7293*G(3,2,2,r) +539700/46189*G(4,2,2,r) +722736/20995*G(5,2,2,r) -803144/1615*G(6,2,2,r) +250368/323*G(7,2,2,r) +5641812/437*G(8,2,2,r) +814000/23*G(9,2,2,r) +26365416/575*G(10,2,2,r) +798336/25*G(11,2,2,r) +104104/9*G(12,2,2,r) +1716*G(13,2,2,r) R(13,3,r) = -2/65*G(0,2,2,r) +477/1820*G(1,2,2,r) -1143/1309*G(2,2,2,r) -2087/2431*G(3,2,2,r) +1011825/46189*G(4,2,2,r) -2572731/41990*G(5,2,2,r) -566868/1615*G(6,2,2,r) +572436/323*G(7,2,2,r) +37782558/3059*G(8,2,2,r) +9362925/322*G(9,2,2,r) +20427462/575*G(10,2,2,r) +603702/25*G(11,2,2,r) +26026/3*G(12,2,2,r) +1287*G(13,2,2,r) R(13,5,r) = +2/39*G(0,2,2,r) -107/364*G(1,2,2,r) -1455/17017*G(2,2,2,r) +124375/21879*G(3,2,2,r) -346075/46189*G(4,2,2,r) -54243/494*G(5,2,2,r) +39420/323*G(6,2,2,r) +888300/323*G(7,2,2,r) +30857310/3059*G(8,2,2,r) +18377755/966*G(9,2,2,r) +2414918/115*G(10,2,2,r) +68178/5*G(11,2,2,r) +130130/27*G(12,2,2,r) +715*G(13,2,2,r) R(13,7,r) = -14/195*G(0,2,2,r) +199/910*G(1,2,2,r) +20634/17017*G(2,2,2,r) -77852/21879*G(3,2,2,r) -1225990/46189*G(4,2,2,r) +395766/20995*G(5,2,2,r) +979236/1615*G(6,2,2,r) +846828/323*G(7,2,2,r) +19060074/3059*G(8,2,2,r) +4533980/483*G(9,2,2,r) +228932/25*G(10,2,2,r) +139656/25*G(11,2,2,r) +52052/27*G(12,2,2,r) +286*G(13,2,2,r) R(13,9,r) = +6/65*G(0,2,2,r) -33/910*G(1,2,2,r) -2658/1547*G(2,2,2,r) -2852/663*G(3,2,2,r) +68190/4199*G(4,2,2,r) +3302838/20995*G(5,2,2,r) +988548/1615*G(6,2,2,r) +490644/323*G(7,2,2,r) +8046522/3059*G(8,2,2,r) +520740/161*G(9,2,2,r) +1594428/575*G(10,2,2,r) +39288/25*G(11,2,2,r) +4732/9*G(12,2,2,r) +78*G(13,2,2,r) R(13,11,r) = -22/195*G(0,2,2,r) -461/1820*G(1,2,2,r) +1257/1547*G(2,2,2,r) +17699/1989*G(3,2,2,r) +168685/4199*G(4,2,2,r) +5160771/41990*G(5,2,2,r) +453508/1615*G(6,2,2,r) +9372/19*G(7,2,2,r) +2043162/3059*G(8,2,2,r) +663685/966*G(9,2,2,r) +298738/575*G(10,2,2,r) +6798/25*G(11,2,2,r) +2366/27*G(12,2,2,r) +13*G(13,2,2,r) R(13,13,r) = +2/15*G(0,2,2,r) +13/20*G(1,2,2,r) +39/17*G(2,2,2,r) +1001/153*G(3,2,2,r) +5005/323*G(4,2,2,r) +99099/3230*G(5,2,2,r) +81796/1615*G(6,2,2,r) +22308/323*G(7,2,2,r) +33462/437*G(8,2,2,r) +9295/138*G(9,2,2,r) +26026/575*G(10,2,2,r) +546/25*G(11,2,2,r) +182/27*G(12,2,2,r) +1*G(13,2,2,r) R(14,0,r) = +12/1105*G(1,2,2,r) -48/221*G(2,2,2,r) +111160/46189*G(3,2,2,r) -841680/46189*G(4,2,2,r) +374808/4199*G(5,2,2,r) -219072/1615*G(6,2,2,r) -622512/391*G(7,2,2,r) +3131040/437*G(8,2,2,r) +5601816/115*G(9,2,2,r) +12218976/115*G(10,2,2,r) +8952944/75*G(11,2,2,r) +224224/3*G(12,2,2,r) +720720/29*G(13,2,2,r) +3432*G(14,2,2,r) R(14,2,r) = +1/56*G(0,2,2,r) -2811/15470*G(1,2,2,r) +5913/6188*G(2,2,2,r) -120570/46189*G(3,2,2,r) -836595/184756*G(4,2,2,r) +355785/4199*G(5,2,2,r) -926667/3230*G(6,2,2,r) -59288328/52003*G(7,2,2,r) +103840935/12236*G(8,2,2,r) +37523673/805*G(9,2,2,r) +22144023/230*G(10,2,2,r) +7934212/75*G(11,2,2,r) +393679/6*G(12,2,2,r) +630630/29*G(13,2,2,r) +3003*G(14,2,2,r) R(14,4,r) = -1/28*G(0,2,2,r) +411/1547*G(1,2,2,r) -2560/4641*G(2,2,2,r) -391810/138567*G(3,2,2,r) +949125/46189*G(4,2,2,r) -818/4199*G(5,2,2,r) -142107/323*G(6,2,2,r) +764280/2737*G(7,2,2,r) +65826255/6118*G(8,2,2,r) +31719182/805*G(9,2,2,r) +8149746/115*G(10,2,2,r) +3294148/45*G(11,2,2,r) +397540/9*G(12,2,2,r) +420420/29*G(13,2,2,r) +2002*G(14,2,2,r) R(14,6,r) = +3/56*G(0,2,2,r) -813/3094*G(1,2,2,r) -7415/18564*G(2,2,2,r) +57430/10659*G(3,2,2,r) +435003/184756*G(4,2,2,r) -444001/4199*G(5,2,2,r) -77553/646*G(6,2,2,r) +104579640/52003*G(7,2,2,r) +131790945/12236*G(8,2,2,r) +21909591/805*G(9,2,2,r) +9455721/230*G(10,2,2,r) +349492/9*G(11,2,2,r) +403975/18*G(12,2,2,r) +210210/29*G(13,2,2,r) +1001*G(14,2,2,r) R(14,8,r) = -1/14*G(0,2,2,r) +1338/7735*G(1,2,2,r) +6044/4641*G(2,2,2,r) -24980/12597*G(3,2,2,r) -112692/4199*G(4,2,2,r) -4796/221*G(5,2,2,r) +741972/1615*G(6,2,2,r) +135204696/52003*G(7,2,2,r) +23145540/3059*G(8,2,2,r) +11401324/805*G(9,2,2,r) +2061312/115*G(10,2,2,r) +3432728/225*G(11,2,2,r) +75088/9*G(12,2,2,r) +76440/29*G(13,2,2,r) +364*G(14,2,2,r) R(14,10,r) = +5/56*G(0,2,2,r) +57/15470*G(1,2,2,r) -28993/18564*G(2,2,2,r) -63530/12597*G(3,2,2,r) +151503/16796*G(4,2,2,r) +572209/4199*G(5,2,2,r) +1978053/3230*G(6,2,2,r) +90074952/52003*G(7,2,2,r) +42503835/12236*G(8,2,2,r) +4105981/805*G(9,2,2,r) +1258851/230*G(10,2,2,r) +940316/225*G(11,2,2,r) +38597/18*G(12,2,2,r) +19110/29*G(13,2,2,r) +91*G(14,2,2,r) R(14,12,r) = -3/28*G(0,2,2,r) -159/595*G(1,2,2,r) +208/357*G(2,2,2,r) +7670/969*G(3,2,2,r) +12441/323*G(4,2,2,r) +40898/323*G(5,2,2,r) +507507/1615*G(6,2,2,r) +31721976/52003*G(7,2,2,r) +5716425/6118*G(8,2,2,r) +903474/805*G(9,2,2,r) +119262/115*G(10,2,2,r) +160108/225*G(11,2,2,r) +3068/9*G(12,2,2,r) +2940/29*G(13,2,2,r) +14*G(14,2,2,r) R(14,14,r) = +1/8*G(0,2,2,r) +21/34*G(1,2,2,r) +455/204*G(2,2,2,r) +6370/969*G(3,2,2,r) +21021/1292*G(4,2,2,r) +11011/323*G(5,2,2,r) +39039/646*G(6,2,2,r) +669240/7429*G(7,2,2,r) +195195/1748*G(8,2,2,r) +13013/115*G(9,2,2,r) +21021/230*G(10,2,2,r) +2548/45*G(11,2,2,r) +455/18*G(12,2,2,r) +210/29*G(13,2,2,r) +1*G(14,2,2,r) R(15,1,r) = -2/255*G(0,2,2,r) +8/85*G(1,2,2,r) -2844/4199*G(2,2,2,r) +45248/12597*G(3,2,2,r) -581700/46189*G(4,2,2,r) +87696/20995*G(5,2,2,r) +564872/1955*G(6,2,2,r) -11844096/7429*G(7,2,2,r) -809028/437*G(8,2,2,r) +935440/23*G(9,2,2,r) +94870776/575*G(10,2,2,r) +7303296/25*G(11,2,2,r) +74850776/261*G(12,2,2,r) +4708704/29*G(13,2,2,r) +1544400/31*G(14,2,2,r) +6435*G(15,2,2,r) R(15,3,r) = +2/85*G(0,2,2,r) -251/1190*G(1,2,2,r) +24454/29393*G(2,2,2,r) -6434/12597*G(3,2,2,r) -647250/46189*G(4,2,2,r) +1568217/20995*G(5,2,2,r) +619696/37145*G(6,2,2,r) -12870792/7429*G(7,2,2,r) +5511528/3059*G(8,2,2,r) +7036865/161*G(9,2,2,r) +250817996/1725*G(10,2,2,r) +17962516/75*G(11,2,2,r) +59391332/261*G(12,2,2,r) +3681678/29*G(13,2,2,r) +1201200/31*G(14,2,2,r) +5005*G(15,2,2,r) R(15,5,r) = -2/51*G(0,2,2,r) +61/238*G(1,2,2,r) -7170/29393*G(2,2,2,r) -148195/37791*G(3,2,2,r) +695330/46189*G(4,2,2,r) +187173/4199*G(5,2,2,r) -2725800/7429*G(6,2,2,r) -6088500/7429*G(7,2,2,r) +21882564/3059*G(8,2,2,r) +20711867/483*G(9,2,2,r) +12502204/115*G(10,2,2,r) +793078/5*G(11,2,2,r) +111131020/783*G(12,2,2,r) +2232230/29*G(13,2,2,r) +720720/31*G(14,2,2,r) +3003*G(15,2,2,r) R(15,7,r) = +14/255*G(0,2,2,r) -137/595*G(1,2,2,r) -18504/29393*G(2,2,2,r) +176837/37791*G(3,2,2,r) +2140/221*G(4,2,2,r) -106722/1235*G(5,2,2,r) -10263792/37145*G(6,2,2,r) +8723484/7429*G(7,2,2,r) +31067784/3059*G(8,2,2,r) +16119290/483*G(9,2,2,r) +37476296/575*G(10,2,2,r) +2061566/25*G(11,2,2,r) +53395888/783*G(12,2,2,r) +1030484/29*G(13,2,2,r) +327600/31*G(14,2,2,r) +1365*G(15,2,2,r) R(15,9,r) = -6/85*G(0,2,2,r) +79/595*G(1,2,2,r) +39128/29393*G(2,2,2,r) -2631/4199*G(3,2,2,r) -105660/4199*G(4,2,2,r) -1067682/20995*G(5,2,2,r) +35728/115*G(6,2,2,r) +17940582/7429*G(7,2,2,r) +25816032/3059*G(8,2,2,r) +3046230/161*G(9,2,2,r) +50760424/1725*G(10,2,2,r) +2416154/75*G(11,2,2,r) +2119936/87*G(12,2,2,r) +350532/29*G(13,2,2,r) +109200/31*G(14,2,2,r) +455*G(15,2,2,r) R(15,11,r) = +22/255*G(0,2,2,r) +43/1190*G(1,2,2,r) -3174/2261*G(2,2,2,r) -15943/2907*G(3,2,2,r) +970/323*G(4,2,2,r) +185031/1615*G(5,2,2,r) +22046024/37145*G(6,2,2,r) +13993122/7429*G(7,2,2,r) +13070772/3059*G(8,2,2,r) +3499925/483*G(9,2,2,r) +5330468/575*G(10,2,2,r) +221078/25*G(11,2,2,r) +4772404/783*G(12,2,2,r) +82922/29*G(13,2,2,r) +25200/31*G(14,2,2,r) +105*G(15,2,2,r) R(15,13,r) = -26/255*G(0,2,2,r) -47/170*G(1,2,2,r) +126/323*G(2,2,2,r) +20384/2907*G(3,2,2,r) +11830/323*G(4,2,2,r) +207207/1615*G(5,2,2,r) +12700688/37145*G(6,2,2,r) +5365074/7429*G(7,2,2,r) +535392/437*G(8,2,2,r) +5005/3*G(9,2,2,r) +1037036/575*G(10,2,2,r) +37856/25*G(11,2,2,r) +745108/783*G(12,2,2,r) +12194/29*G(13,2,2,r) +3600/31*G(14,2,2,r) +15*G(15,2,2,r) R(15,15,r) = +2/17*G(0,2,2,r) +10/17*G(1,2,2,r) +700/323*G(2,2,2,r) +6370/969*G(3,2,2,r) +5460/323*G(4,2,2,r) +12012/323*G(5,2,2,r) +520520/7429*G(6,2,2,r) +836550/7429*G(7,2,2,r) +66924/437*G(8,2,2,r) +4004/23*G(9,2,2,r) +56056/345*G(10,2,2,r) +364/3*G(11,2,2,r) +18200/261*G(12,2,2,r) +840/29*G(13,2,2,r) +240/31*G(14,2,2,r) +1*G(15,2,2,r) R(16,0,r) = -12/1615*G(1,2,2,r) +48/323*G(2,2,2,r) -7000/4199*G(3,2,2,r) +55440/4199*G(4,2,2,r) -7179480/96577*G(5,2,2,r) +8766912/37145*G(6,2,2,r) +2516976/7429*G(7,2,2,r) -3120480/437*G(8,2,2,r) +616616/69*G(9,2,2,r) +4068064/23*G(10,2,2,r) +390806416/725*G(11,2,2,r) +71079008/87*G(12,2,2,r) +645044400/899*G(13,2,2,r) +11531520/31*G(14,2,2,r) +106080*G(15,2,2,r) +12870*G(16,2,2,r) R(16,2,r) = -1/72*G(0,2,2,r) +1399/9690*G(1,2,2,r) -1039/1292*G(2,2,2,r) +101570/37791*G(3,2,2,r) -15785/16796*G(4,2,2,r) -5083617/96577*G(5,2,2,r) +69615161/222870*G(6,2,2,r) -1688632/7429*G(7,2,2,r) -11500335/1748*G(8,2,2,r) +9307441/621*G(9,2,2,r) +73188115/414*G(10,2,2,r) +1093976884/2175*G(11,2,2,r) +1161387227/1566*G(12,2,2,r) +578027450/899*G(13,2,2,r) +10272405/31*G(14,2,2,r) +282880/3*G(15,2,2,r) +11440*G(16,2,2,r) R(16,4,r) = +1/36*G(0,2,2,r) -215/969*G(1,2,2,r) +1420/2261*G(2,2,2,r) +46430/37791*G(3,2,2,r) -71645/4199*G(4,2,2,r) +3817506/96577*G(5,2,2,r) +294217/1311*G(6,2,2,r) -10049512/7429*G(7,2,2,r) -2991879/874*G(8,2,2,r) +125201362/4347*G(9,2,2,r) +173753866/1035*G(10,2,2,r) +175467292/435*G(11,2,2,r) +431971540/783*G(12,2,2,r) +414393980/899*G(13,2,2,r) +7237230/31*G(14,2,2,r) +198016/3*G(15,2,2,r) +8008*G(16,2,2,r) R(16,6,r) = -1/24*G(0,2,2,r) +155/646*G(1,2,2,r) +205/9044*G(2,2,2,r) -54790/12597*G(3,2,2,r) +80745/9724*G(4,2,2,r) +6707001/96577*G(5,2,2,r) -194887/874*G(6,2,2,r) -10386552/7429*G(7,2,2,r) +5276007/1748*G(8,2,2,r) +56741971/1449*G(9,2,2,r) +94742219/690*G(10,2,2,r) +116979772/435*G(11,2,2,r) +172716635/522*G(12,2,2,r) +234919230/899*G(13,2,2,r) +3989895/31*G(14,2,2,r) +396032/11*G(15,2,2,r) +4368*G(16,2,2,r) R(16,8,r) = +1/18*G(0,2,2,r) -962/4845*G(1,2,2,r) -1788/2261*G(2,2,2,r) +8420/2223*G(3,2,2,r) +672700/46189*G(4,2,2,r) -5867820/96577*G(5,2,2,r) -39681796/111435*G(6,2,2,r) +2928904/7429*G(7,2,2,r) +198000/23*G(8,2,2,r) +158857556/4347*G(9,2,2,r) +18406960/207*G(10,2,2,r) +103356344/725*G(11,2,2,r) +121878848/783*G(12,2,2,r) +103066600/899*G(13,2,2,r) +1687140/31*G(14,2,2,r) +495040/33*G(15,2,2,r) +1820*G(16,2,2,r) R(16,10,r) = -5/72*G(0,2,2,r) +947/9690*G(1,2,2,r) +11931/9044*G(2,2,2,r) +1450/2907*G(3,2,2,r) -317975/14212*G(4,2,2,r) -521325/7429*G(5,2,2,r) +38599561/222870*G(6,2,2,r) +685256/323*G(7,2,2,r) +15437565/1748*G(8,2,2,r) +100593779/4347*G(9,2,2,r) +17654351/414*G(10,2,2,r) +41312908/725*G(11,2,2,r) +86287747/1566*G(12,2,2,r) +33763450/899*G(13,2,2,r) +528885/31*G(14,2,2,r) +152320/33*G(15,2,2,r) +560*G(16,2,2,r) R(16,12,r) = +1/12*G(0,2,2,r) +101/1615*G(1,2,2,r) -404/323*G(2,2,2,r) -5530/969*G(3,2,2,r) -6825/3553*G(4,2,2,r) +693966/7429*G(5,2,2,r) +20833813/37145*G(6,2,2,r) +14678664/7429*G(7,2,2,r) +4356495/874*G(8,2,2,r) +1973686/207*G(9,2,2,r) +970970/69*G(10,2,2,r) +34777652/2175*G(11,2,2,r) +3588676/261*G(12,2,2,r) +7772100/899*G(13,2,2,r) +115890/31*G(14,2,2,r) +10880/11*G(15,2,2,r) +120*G(16,2,2,r) R(16,14,r) = -7/72*G(0,2,2,r) -547/1938*G(1,2,2,r) +295/1292*G(2,2,2,r) +17990/2907*G(3,2,2,r) +491855/14212*G(4,2,2,r) +953589/7429*G(5,2,2,r) +16227211/44574*G(6,2,2,r) +6142136/7429*G(7,2,2,r) +2673099/1748*G(8,2,2,r) +1435291/621*G(9,2,2,r) +5874869/2070*G(10,2,2,r) +1214668/435*G(11,2,2,r) +3366545/1566*G(12,2,2,r) +1120910/899*G(13,2,2,r) +15855/31*G(14,2,2,r) +4352/33*G(15,2,2,r) +16*G(16,2,2,r) R(16,16,r) = +1/9*G(0,2,2,r) +32/57*G(1,2,2,r) +40/19*G(2,2,2,r) +1120/171*G(3,2,2,r) +3640/209*G(4,2,2,r) +17472/437*G(5,2,2,r) +104104/1311*G(6,2,2,r) +59488/437*G(7,2,2,r) +87516/437*G(8,2,2,r) +155584/621*G(9,2,2,r) +272272/1035*G(10,2,2,r) +99008/435*G(11,2,2,r) +123760/783*G(12,2,2,r) +76160/899*G(13,2,2,r) +1020/31*G(14,2,2,r) +272/33*G(15,2,2,r) +1*G(16,2,2,r) R(17,1,r) = +2/323*G(0,2,2,r) -24/323*G(1,2,2,r) +1220/2261*G(2,2,2,r) -960/323*G(3,2,2,r) +1152900/96577*G(4,2,2,r) -2103024/96577*G(5,2,2,r) -4954488/37145*G(6,2,2,r) +9985536/7429*G(7,2,2,r) -4493060/1311*G(8,2,2,r) -9826960/483*G(9,2,2,r) +337263784/3335*G(10,2,2,r) +296103808/435*G(11,2,2,r) +1456935480/899*G(12,2,2,r) +1907025120/899*G(13,2,2,r) +51932400/31*G(14,2,2,r) +798720*G(15,2,2,r) +1487772/7*G(16,2,2,r) +24310*G(17,2,2,r) R(17,3,r) = -6/323*G(0,2,2,r) +1117/6460*G(1,2,2,r) -1719/2261*G(2,2,2,r) +1175/969*G(3,2,2,r) +775005/96577*G(4,2,2,r) -12738033/193154*G(5,2,2,r) +26309668/185725*G(6,2,2,r) +31691484/37145*G(7,2,2,r) -7432282/1311*G(8,2,2,r) -9918337/966*G(9,2,2,r) +255357674/2001*G(10,2,2,r) +1391624234/2175*G(11,2,2,r) +11289480202/8091*G(12,2,2,r) +1577100525/899*G(13,2,2,r) +42095040/31*G(14,2,2,r) +641264*G(15,2,2,r) +5951088/35*G(16,2,2,r) +19448*G(17,2,2,r) R(17,5,r) = +10/323*G(0,2,2,r) -1431/6460*G(1,2,2,r) +131/323*G(2,2,2,r) +26075/10659*G(3,2,2,r) -16831605/1062347*G(4,2,2,r) +313635/193154*G(5,2,2,r) +2466492/8075*G(6,2,2,r) -21731292/37145*G(7,2,2,r) -7697690/1311*G(8,2,2,r) +1353781/138*G(9,2,2,r) +102780678/667*G(10,2,2,r) +1170960518/2175*G(11,2,2,r) +8231595554/8091*G(12,2,2,r) +1069620825/899*G(13,2,2,r) +302352960/341*G(14,2,2,r) +4520880/11*G(15,2,2,r) +541008/5*G(16,2,2,r) +12376*G(17,2,2,r) R(17,7,r) = -14/323*G(0,2,2,r) +711/3230*G(1,2,2,r) +78/323*G(2,2,2,r) -46060/10659*G(3,2,2,r) +1957830/1062347*G(4,2,2,r) +23226/299*G(5,2,2,r) -12718692/185725*G(6,2,2,r) -56945196/37145*G(7,2,2,r) -799942/1311*G(8,2,2,r) +2091232/69*G(9,2,2,r) +498734236/3335*G(10,2,2,r) +826988344/2175*G(11,2,2,r) +4938556532/8091*G(12,2,2,r) +584932530/899*G(13,2,2,r) +156942240/341*G(14,2,2,r) +2284464/11*G(15,2,2,r) +270504/5*G(16,2,2,r) +6188*G(17,2,2,r) R(17,9,r) = +18/323*G(0,2,2,r) -109/646*G(1,2,2,r) -290/323*G(2,2,2,r) +30380/10659*G(3,2,2,r) +1421070/81719*G(4,2,2,r) -254394/7429*G(5,2,2,r) -823732/2185*G(6,2,2,r) -1848132/7429*G(7,2,2,r) +8578570/1311*G(8,2,2,r) +2528240/69*G(9,2,2,r) +1086801716/10005*G(10,2,2,r) +92414504/435*G(11,2,2,r) +2348096660/8091*G(12,2,2,r) +251118210/899*G(13,2,2,r) +63319200/341*G(14,2,2,r) +890960/11*G(15,2,2,r) +20808*G(16,2,2,r) +2380*G(17,2,2,r) R(17,11,r) = -22/323*G(0,2,2,r) +87/1292*G(1,2,2,r) +2895/2261*G(2,2,2,r) +15005/10659*G(3,2,2,r) -1555995/81719*G(4,2,2,r) -63777/782*G(5,2,2,r) +1990716/37145*G(6,2,2,r) +13132548/7429*G(7,2,2,r) +11524370/1311*G(8,2,2,r) +25584845/966*G(9,2,2,r) +188006962/3335*G(10,2,2,r) +38592554/435*G(11,2,2,r) +843388910/8091*G(12,2,2,r) +81287535/899*G(13,2,2,r) +19147200/341*G(14,2,2,r) +258960/11*G(15,2,2,r) +41616/7*G(16,2,2,r) +680*G(17,2,2,r) R(17,13,r) = +26/323*G(0,2,2,r) +543/6460*G(1,2,2,r) -2501/2261*G(2,2,2,r) -61525/10659*G(3,2,2,r) -481215/81719*G(4,2,2,r) +1092273/14858*G(5,2,2,r) +96405036/185725*G(6,2,2,r) +74857068/37145*G(7,2,2,r) +7319026/1311*G(8,2,2,r) +11435281/966*G(9,2,2,r) +2854566/145*G(10,2,2,r) +56104958/2175*G(11,2,2,r) +213678374/8091*G(12,2,2,r) +18606315/899*G(13,2,2,r) +4082880/341*G(14,2,2,r) +52848/11*G(15,2,2,r) +41616/35*G(16,2,2,r) +136*G(17,2,2,r) R(17,15,r) = -30/323*G(0,2,2,r) -461/1615*G(1,2,2,r) +208/2261*G(2,2,2,r) +58000/10659*G(3,2,2,r) +2659440/81719*G(4,2,2,r) +944580/7429*G(5,2,2,r) +70771792/185725*G(6,2,2,r) +34244496/37145*G(7,2,2,r) +2408120/1311*G(8,2,2,r) +1464892/483*G(9,2,2,r) +8287136/2001*G(10,2,2,r) +10084256/2175*G(11,2,2,r) +33892768/8091*G(12,2,2,r) +2678550/899*G(13,2,2,r) +547320/341*G(14,2,2,r) +6760/11*G(15,2,2,r) +5202/35*G(16,2,2,r) +17*G(17,2,2,r) R(17,17,r) = +2/19*G(0,2,2,r) +51/95*G(1,2,2,r) +272/133*G(2,2,2,r) +1360/209*G(3,2,2,r) +85680/4807*G(4,2,2,r) +18564/437*G(5,2,2,r) +965328/10925*G(6,2,2,r) +350064/2185*G(7,2,2,r) +330616/1311*G(8,2,2,r) +165308/483*G(9,2,2,r) +1322464/3335*G(10,2,2,r) +841568/2175*G(11,2,2,r) +841568/2697*G(12,2,2,r) +182070/899*G(13,2,2,r) +34680/341*G(14,2,2,r) +408/11*G(15,2,2,r) +306/35*G(16,2,2,r) +1*G(17,2,2,r) R(18,0,r) = +12/2261*G(1,2,2,r) -240/2261*G(2,2,2,r) +8920/7429*G(3,2,2,r) -72720/7429*G(4,2,2,r) +28834344/482885*G(5,2,2,r) -9151296/37145*G(6,2,2,r) +2354352/7429*G(7,2,2,r) +11792352/3059*G(8,2,2,r) -110072248/4669*G(9,2,2,r) -104383136/3335*G(10,2,2,r) +2460334448/4495*G(11,2,2,r) +6559673120/2697*G(12,2,2,r) +4366318320/899*G(13,2,2,r) +175069440/31*G(14,2,2,r) +28493088/7*G(15,2,2,r) +12602304/7*G(16,2,2,r) +16628040/37*G(17,2,2,r) +48620*G(18,2,2,r) R(18,2,r) = +1/90*G(0,2,2,r) -3982/33915*G(1,2,2,r) +1541/2261*G(2,2,2,r) -171824/66861*G(3,2,2,r) +28415/7429*G(4,2,2,r) +69888588/2414425*G(5,2,2,r) -144419506/557175*G(6,2,2,r) +28675504/37145*G(7,2,2,r) +35272809/15295*G(8,2,2,r) -3172382356/126063*G(9,2,2,r) -1562364518/150075*G(10,2,2,r) +38794385344/67425*G(11,2,2,r) +56580089566/24273*G(12,2,2,r) +4047804488/899*G(13,2,2,r) +159722940/31*G(14,2,2,r) +386760608/105*G(15,2,2,r) +56795453/35*G(16,2,2,r) +14965236/37*G(17,2,2,r) +43758*G(18,2,2,r) R(18,4,r) = -1/45*G(0,2,2,r) +6344/33915*G(1,2,2,r) -31589/49742*G(2,2,2,r) -152602/735471*G(3,2,2,r) +2089595/163438*G(4,2,2,r) -125441736/2414425*G(5,2,2,r) -26388418/557175*G(6,2,2,r) +45155032/37145*G(7,2,2,r) -32508333/15295*G(8,2,2,r) -2900075464/126063*G(9,2,2,r) +6949802431/150075*G(10,2,2,r) +41736900452/67425*G(11,2,2,r) +48992537503/24273*G(12,2,2,r) +35261952544/9889*G(13,2,2,r) +1329846960/341*G(14,2,2,r) +3144578944/1155*G(15,2,2,r) +41491424/35*G(16,2,2,r) +10883808/37*G(17,2,2,r) +31824*G(18,2,2,r) R(18,6,r) = +1/30*G(0,2,2,r) -346/1615*G(1,2,2,r) +689/3553*G(2,2,2,r) +779576/245157*G(3,2,2,r) -2015895/163438*G(4,2,2,r) -3659334/127075*G(5,2,2,r) +53783009/185725*G(6,2,2,r) +6246552/37145*G(7,2,2,r) -25725843/4370*G(8,2,2,r) -39605566/6003*G(9,2,2,r) +5615206597/50025*G(10,2,2,r) +40211570672/67425*G(11,2,2,r) +12279503236/8091*G(12,2,2,r) +23455889184/9889*G(13,2,2,r) +826775040/341*G(14,2,2,r) +89687104/55*G(15,2,2,r) +3483402/5*G(16,2,2,r) +6348888/37*G(17,2,2,r) +18564*G(18,2,2,r) R(18,8,r) = -2/45*G(0,2,2,r) +964/4845*G(1,2,2,r) +1473/3553*G(2,2,2,r) -2944844/735471*G(3,2,2,r) -15610/4301*G(4,2,2,r) +13777596/185725*G(5,2,2,r) +36096424/557175*G(6,2,2,r) -50687416/37145*G(7,2,2,r) -7083648/2185*G(8,2,2,r) +343010668/18009*G(9,2,2,r) +21663513872/150075*G(10,2,2,r) +10533105128/22475*G(11,2,2,r) +22962747626/24273*G(12,2,2,r) +12775077728/9889*G(13,2,2,r) +414963360/341*G(14,2,2,r) +128713664/165*G(15,2,2,r) +1624384/5*G(16,2,2,r) +2930256/37*G(17,2,2,r) +8568*G(18,2,2,r) R(18,10,r) = +1/18*G(0,2,2,r) -958/6783*G(1,2,2,r) -23955/24871*G(2,2,2,r) +1430200/735471*G(3,2,2,r) +3043225/163438*G(4,2,2,r) -366786/37145*G(5,2,2,r) -39783289/111435*G(6,2,2,r) -5403944/7429*G(7,2,2,r) +1388673/322*G(8,2,2,r) +4301842402/126063*G(9,2,2,r) +3660062263/30015*G(10,2,2,r) +1274219024/4495*G(11,2,2,r) +11327219540/24273*G(12,2,2,r) +5509165760/9889*G(13,2,2,r) +163771920/341*G(14,2,2,r) +67269952/231*G(15,2,2,r) +822902/7*G(16,2,2,r) +1046520/37*G(17,2,2,r) +3060*G(18,2,2,r) R(18,12,r) = -1/15*G(0,2,2,r) +464/11305*G(1,2,2,r) +60913/49742*G(2,2,2,r) +521078/245157*G(3,2,2,r) -2538615/163438*G(4,2,2,r) -16123128/185725*G(5,2,2,r) -369278/8075*G(6,2,2,r) +51666888/37145*G(7,2,2,r) +128415573/15295*G(8,2,2,r) +1209833768/42021*G(9,2,2,r) +3476922163/50025*G(10,2,2,r) +8467215068/67425*G(11,2,2,r) +1400712859/8091*G(12,2,2,r) +1798650336/9889*G(13,2,2,r) +48847440/341*G(14,2,2,r) +31480192/385*G(15,2,2,r) +1114656/35*G(16,2,2,r) +279072/37*G(17,2,2,r) +816*G(18,2,2,r) R(18,14,r) = +7/90*G(0,2,2,r) +3446/33915*G(1,2,2,r) -24163/24871*G(2,2,2,r) -4210768/735471*G(3,2,2,r) -738680/81719*G(4,2,2,r) +10261776/185725*G(5,2,2,r) +262842944/557175*G(6,2,2,r) +74654944/37145*G(7,2,2,r) +4875156/805*G(8,2,2,r) +1770962336/126063*G(9,2,2,r) +3882396232/150075*G(10,2,2,r) +2574794144/67425*G(11,2,2,r) +1094265991/24273*G(12,2,2,r) +415855468/9889*G(13,2,2,r) +10332210/341*G(14,2,2,r) +18759568/1155*G(15,2,2,r) +425731/70*G(16,2,2,r) +52326/37*G(17,2,2,r) +153*G(18,2,2,r) R(18,16,r) = -4/45*G(0,2,2,r) -572/1995*G(1,2,2,r) -34/1463*G(2,2,2,r) +206176/43263*G(3,2,2,r) +146540/4807*G(4,2,2,r) +1365168/10925*G(5,2,2,r) +12895792/32775*G(6,2,2,r) +2199392/2185*G(7,2,2,r) +32730984/15295*G(8,2,2,r) +480715664/126063*G(9,2,2,r) +855303592/150075*G(10,2,2,r) +479212864/67425*G(11,2,2,r) +177623446/24273*G(12,2,2,r) +60479608/9889*G(13,2,2,r) +1379040/341*G(14,2,2,r) +2349808/1155*G(15,2,2,r) +25568/35*G(16,2,2,r) +6156/37*G(17,2,2,r) +18*G(18,2,2,r) R(18,18,r) = +1/10*G(0,2,2,r) +18/35*G(1,2,2,r) +153/77*G(2,2,2,r) +1632/253*G(3,2,2,r) +4590/253*G(4,2,2,r) +25704/575*G(5,2,2,r) +55692/575*G(6,2,2,r) +21216/115*G(7,2,2,r) +247962/805*G(8,2,2,r) +6281704/14007*G(9,2,2,r) +9422556/16675*G(10,2,2,r) +13705536/22475*G(11,2,2,r) +499681/899*G(12,2,2,r) +4151196/9889*G(13,2,2,r) +87210/341*G(14,2,2,r) +46512/385*G(15,2,2,r) +2907/70*G(16,2,2,r) +342/37*G(17,2,2,r) +1*G(18,2,2,r) R(19,1,r) = -2/399*G(0,2,2,r) +8/133*G(1,2,2,r) -22860/52003*G(2,2,2,r) +55360/22287*G(3,2,2,r) -402036/37145*G(4,2,2,r) +1078704/37145*G(5,2,2,r) +3979976/111435*G(6,2,2,r) -47810048/52003*G(7,2,2,r) +405266004/88711*G(8,2,2,r) -110370832/210105*G(9,2,2,r) -31241755688/310155*G(10,2,2,r) +616497024/4495*G(11,2,2,r) +19996032680/8091*G(12,2,2,r) +7193615520/899*G(13,2,2,r) +2945597616/217*G(14,2,2,r) +98668544/7*G(15,2,2,r) +2410686564/259*G(16,2,2,r) +141775920/37*G(17,2,2,r) +2700280/3*G(18,2,2,r) +92378*G(19,2,2,r) R(19,3,r) = +2/133*G(0,2,2,r) -1054/7315*G(1,2,2,r) +391156/572033*G(2,2,2,r) -380360/245157*G(3,2,2,r) -1568724/408595*G(4,2,2,r) +1928796/37145*G(5,2,2,r) -36227464/185725*G(6,2,2,r) -39203424/260015*G(7,2,2,r) +420948372/88711*G(8,2,2,r) -267502092/23345*G(9,2,2,r) -25833090712/310155*G(10,2,2,r) +17915017328/67425*G(11,2,2,r) +220772645704/89001*G(12,2,2,r) +71195986680/9889*G(13,2,2,r) +27788324304/2387*G(14,2,2,r) +908016512/77*G(15,2,2,r) +9951977412/1295*G(16,2,2,r) +116292852/37*G(17,2,2,r) +736440*G(18,2,2,r) +75582*G(19,2,2,r) R(19,5,r) = -10/399*G(0,2,2,r) +1402/7315*G(1,2,2,r) -273228/572033*G(2,2,2,r) -1985465/1470942*G(3,2,2,r) +5736134/408595*G(4,2,2,r) -58518/2185*G(5,2,2,r) -33126548/185725*G(6,2,2,r) +265954182/260015*G(7,2,2,r) +123469242/88711*G(8,2,2,r) -1594935914/70035*G(9,2,2,r) -2939749956/103385*G(10,2,2,r) +10104599167/22475*G(11,2,2,r) +624593853104/267003*G(12,2,2,r) +56503021120/9889*G(13,2,2,r) +20262149856/2387*G(14,2,2,r) +632146632/77*G(15,2,2,r) +6754755384/1295*G(16,2,2,r) +77921064/37*G(17,2,2,r) +490960*G(18,2,2,r) +50388*G(19,2,2,r) R(19,7,r) = +2/57*G(0,2,2,r) -212/1045*G(1,2,2,r) +468/81719*G(2,2,2,r) +5186125/1470942*G(3,2,2,r) -3234574/408595*G(4,2,2,r) -1239588/25415*G(5,2,2,r) +40398316/185725*G(6,2,2,r) +26680758/37145*G(7,2,2,r) -55620474/12673*G(8,2,2,r) -172039868/10005*G(9,2,2,r) +5986864884/103385*G(10,2,2,r) +12666001621/22475*G(11,2,2,r) +511848816752/267003*G(12,2,2,r) +42620480/11*G(13,2,2,r) +1765287072/341*G(14,2,2,r) +51745416/11*G(15,2,2,r) +533454696/185*G(16,2,2,r) +42274512/37*G(17,2,2,r) +3436720/13*G(18,2,2,r) +27132*G(19,2,2,r) R(19,9,r) = -6/133*G(0,2,2,r) +260/1463*G(1,2,2,r) +313100/572033*G(2,2,2,r) -575215/163438*G(3,2,2,r) -140202/17765*G(4,2,2,r) +30642492/482885*G(5,2,2,r) +53060/323*G(6,2,2,r) -53399970/52003*G(7,2,2,r) -424439886/88711*G(8,2,2,r) +179459852/23345*G(9,2,2,r) +38734213804/310155*G(10,2,2,r) +6994901303/13485*G(11,2,2,r) +12704491280/9889*G(12,2,2,r) +21409194240/9889*G(13,2,2,r) +6157687776/2387*G(14,2,2,r) +167857864/77*G(15,2,2,r) +331159320/259*G(16,2,2,r) +18298800/37*G(17,2,2,r) +1472880/13*G(18,2,2,r) +11628*G(19,2,2,r) R(19,11,r) = +22/399*G(0,2,2,r) -170/1463*G(1,2,2,r) -570300/572033*G(2,2,2,r) +1635115/1470942*G(3,2,2,r) +7631438/408595*G(4,2,2,r) +278046/25415*G(5,2,2,r) -11566772/37145*G(6,2,2,r) -3199326/3059*G(7,2,2,r) +192353538/88711*G(8,2,2,r) +2079905542/70035*G(9,2,2,r) +2646241884/20677*G(10,2,2,r) +1562153879/4495*G(11,2,2,r) +179239976240/267003*G(12,2,2,r) +9476101600/9889*G(13,2,2,r) +2430506592/2387*G(14,2,2,r) +61290168/77*G(15,2,2,r) +115005816/259*G(16,2,2,r) +6175080/37*G(17,2,2,r) +490960/13*G(18,2,2,r) +3876*G(19,2,2,r) R(19,13,r) = -26/399*G(0,2,2,r) +134/7315*G(1,2,2,r) +662724/572033*G(2,2,2,r) +1971005/735471*G(3,2,2,r) -4934728/408595*G(4,2,2,r) -42256224/482885*G(5,2,2,r) -23202928/185725*G(6,2,2,r) +264676152/260015*G(7,2,2,r) +29839368/3857*G(8,2,2,r) +2103497968/70035*G(9,2,2,r) +8390134896/103385*G(10,2,2,r) +3713315827/22475*G(11,2,2,r) +69580203524/267003*G(12,2,2,r) +3168927580/9889*G(13,2,2,r) +727921368/2387*G(14,2,2,r) +16952604/77*G(15,2,2,r) +150686334/1295*G(16,2,2,r) +1566414/37*G(17,2,2,r) +122740/13*G(18,2,2,r) +969*G(19,2,2,r) R(19,15,r) = +10/133*G(0,2,2,r) +848/7315*G(1,2,2,r) -28516/33649*G(2,2,2,r) -80755/14421*G(3,2,2,r) -276456/24035*G(4,2,2,r) +47904/1235*G(5,2,2,r) +4606672/10925*G(6,2,2,r) +30098952/15295*G(7,2,2,r) +568063704/88711*G(8,2,2,r) +375501984/23345*G(9,2,2,r) +10037462864/310155*G(10,2,2,r) +3566039867/67425*G(11,2,2,r) +6261291556/89001*G(12,2,2,r) +748386240/9889*G(13,2,2,r) +154904952/2387*G(14,2,2,r) +3334244/77*G(15,2,2,r) +28018278/1295*G(16,2,2,r) +281088/37*G(17,2,2,r) +21660/13*G(18,2,2,r) +171*G(19,2,2,r) R(19,17,r) = -34/399*G(0,2,2,r) -2096/7315*G(1,2,2,r) -4068/33649*G(2,2,2,r) +19975/4807*G(3,2,2,r) +684216/24035*G(4,2,2,r) +3466368/28405*G(5,2,2,r) +13169968/32775*G(6,2,2,r) +16525496/15295*G(7,2,2,r) +215772024/88711*G(8,2,2,r) +42318848/9135*G(9,2,2,r) +2321585552/310155*G(10,2,2,r) +230007297/22475*G(11,2,2,r) +348754796/29667*G(12,2,2,r) +110869920/9889*G(13,2,2,r) +20816568/2387*G(14,2,2,r) +415004/77*G(15,2,2,r) +3294294/1295*G(16,2,2,r) +31824/37*G(17,2,2,r) +7220/39*G(18,2,2,r) +19*G(19,2,2,r) R(19,19,r) = +2/21*G(0,2,2,r) +38/77*G(1,2,2,r) +3420/1771*G(2,2,2,r) +1615/253*G(3,2,2,r) +23256/1265*G(4,2,2,r) +69768/1495*G(5,2,2,r) +36176/345*G(6,2,2,r) +33592/161*G(7,2,2,r) +1713192/4669*G(8,2,2,r) +119352376/210105*G(9,2,2,r) +238704752/310155*G(10,2,2,r) +4068831/4495*G(11,2,2,r) +27125540/29667*G(12,2,2,r) +7732620/9889*G(13,2,2,r) +1325592/2387*G(14,2,2,r) +24548/77*G(15,2,2,r) +36822/259*G(16,2,2,r) +1710/37*G(17,2,2,r) +380/39*G(18,2,2,r) +1*G(19,2,2,r) R(20,0,r) = -12/3059*G(1,2,2,r) +240/3059*G(2,2,2,r) -6632/7429*G(3,2,2,r) +55152/7429*G(4,2,2,r) -15400/323*G(5,2,2,r) +8392384/37145*G(6,2,2,r) -129132432/215441*G(7,2,2,r) -104383136/88711*G(8,2,2,r) +2840159608/144739*G(9,2,2,r) -5539142752/103385*G(10,2,2,r) -1361931792/4495*G(11,2,2,r) +3549247520/2697*G(12,2,2,r) +8803632240/899*G(13,2,2,r) +796872960/31*G(14,2,2,r) +9932546208/259*G(15,2,2,r) +9371913408/259*G(16,2,2,r) +818184840/37*G(17,2,2,r) +8527200*G(18,2,2,r) +77597520/41*G(19,2,2,r) +184756*G(20,2,2,r) R(20,2,r) = -1/110*G(0,2,2,r) +16374/168245*G(1,2,2,r) -19611/33649*G(2,2,2,r) +194704/81719*G(3,2,2,r) -431415/81719*G(4,2,2,r) -2366644/185725*G(5,2,2,r) +35937538/185725*G(6,2,2,r) -957010704/1077205*G(7,2,2,r) +243050041/443555*G(8,2,2,r) +7380131876/434217*G(9,2,2,r) -35483427122/516925*G(10,2,2,r) -61463023232/247225*G(11,2,2,r) +14836372278/9889*G(12,2,2,r) +95269265208/9889*G(13,2,2,r) +8281917540/341*G(14,2,2,r) +506409095712/14245*G(15,2,2,r) +42999731541/1295*G(16,2,2,r) +746676516/37*G(17,2,2,r) +7760398*G(18,2,2,r) +70543200/41*G(19,2,2,r) +167960*G(20,2,2,r) R(20,4,r) = +1/55*G(0,2,2,r) -26808/168245*G(1,2,2,r) +61681/100947*G(2,2,2,r) -4588/10659*G(3,2,2,r) -733575/81719*G(4,2,2,r) +9585968/185725*G(5,2,2,r) -11310936/185725*G(6,2,2,r) -828464832/1077205*G(7,2,2,r) +1748450808/443555*G(8,2,2,r) +2178027904/434217*G(9,2,2,r) -47504397226/516925*G(10,2,2,r) -159557060104/2225025*G(11,2,2,r) +170557944466/89001*G(12,2,2,r) +88759342464/9889*G(13,2,2,r) +6935413160/341*G(14,2,2,r) +402049373856/14245*G(15,2,2,r) +33152655978/1295*G(16,2,2,r) +566469648/37*G(17,2,2,r) +5839194*G(18,2,2,r) +52907400/41*G(19,2,2,r) +125970*G(20,2,2,r) R(20,6,r) = -3/110*G(0,2,2,r) +4566/24035*G(1,2,2,r) -4537/14421*G(2,2,2,r) -531664/245157*G(3,2,2,r) +1444695/111826*G(4,2,2,r) -1666826/2414425*G(5,2,2,r) -44040171/185725*G(6,2,2,r) +601398648/1077205*G(7,2,2,r) +460503693/126730*G(8,2,2,r) -301801994/20677*G(9,2,2,r) -38380252911/516925*G(10,2,2,r) +458652559456/2225025*G(11,2,2,r) +198047188976/89001*G(12,2,2,r) +74540534304/9889*G(13,2,2,r) +5050311040/341*G(14,2,2,r) +38672417088/2035*G(15,2,2,r) +3047560794/185*G(16,2,2,r) +4617920664/481*G(17,2,2,r) +46965492/13*G(18,2,2,r) +32558400/41*G(19,2,2,r) +77520*G(20,2,2,r) R(20,8,r) = +2/55*G(0,2,2,r) -4548/24035*G(1,2,2,r) -2234/14421*G(2,2,2,r) +878752/245157*G(3,2,2,r) -3652635/1062347*G(4,2,2,r) -142155412/2414425*G(5,2,2,r) +22764648/185725*G(6,2,2,r) +1098882216/1077205*G(7,2,2,r) -7537608/3335*G(8,2,2,r) -1339076908/62031*G(9,2,2,r) +2709644938/516925*G(10,2,2,r) +1014619092032/2225025*G(11,2,2,r) +188365631272/89001*G(12,2,2,r) +53575702368/9889*G(13,2,2,r) +100484960/11*G(14,2,2,r) +21737257536/2035*G(15,2,2,r) +1617702048/185*G(16,2,2,r) +2369274768/481*G(17,2,2,r) +23659104/13*G(18,2,2,r) +16279200/41*G(19,2,2,r) +38760*G(20,2,2,r) R(20,10,r) = -1/22*G(0,2,2,r) +5286/33649*G(1,2,2,r) +65215/100947*G(2,2,2,r) -723584/245157*G(3,2,2,r) -23306667/2124694*G(4,2,2,r) +23650606/482885*G(5,2,2,r) +8487537/37145*G(6,2,2,r) -134239176/215441*G(7,2,2,r) -952299309/177422*G(8,2,2,r) -33433010/14973*G(9,2,2,r) +9943314953/103385*G(10,2,2,r) +233772082336/445005*G(11,2,2,r) +140085498280/89001*G(12,2,2,r) +1016687040/319*G(13,2,2,r) +1578722000/341*G(14,2,2,r) +13970602176/2849*G(15,2,2,r) +974297574/259*G(16,2,2,r) +978728760/481*G(17,2,2,r) +9554340/13*G(18,2,2,r) +6511680/41*G(19,2,2,r) +15504*G(20,2,2,r) R(20,12,r) = +3/55*G(0,2,2,r) -15744/168245*G(1,2,2,r) -101677/100947*G(2,2,2,r) +90548/245157*G(3,2,2,r) +19028235/1062347*G(4,2,2,r) +67003216/2414425*G(5,2,2,r) -46776264/185725*G(6,2,2,r) -1318932288/1077205*G(7,2,2,r) +118344252/443555*G(8,2,2,r) +3487658512/144739*G(9,2,2,r) +65649135981/516925*G(10,2,2,r) +886731620164/2225025*G(11,2,2,r) +78862075019/89001*G(12,2,2,r) +14564336016/9889*G(13,2,2,r) +634674940/341*G(14,2,2,r) +25426918224/14245*G(15,2,2,r) +1654751457/1295*G(16,2,2,r) +317700216/481*G(17,2,2,r) +3020373/13*G(18,2,2,r) +2034900/41*G(19,2,2,r) +4845*G(20,2,2,r) R(20,14,r) = -7/110*G(0,2,2,r) -222/168245*G(1,2,2,r) +109729/100947*G(2,2,2,r) +44672/14421*G(3,2,2,r) -550500/62491*G(4,2,2,r) -12061616/142025*G(5,2,2,r) -2027136/10925*G(6,2,2,r) +42223968/63365*G(7,2,2,r) +3058798236/443555*G(8,2,2,r) +13151635744/434217*G(9,2,2,r) +46901740028/516925*G(10,2,2,r) +456630083312/2225025*G(11,2,2,r) +32349225727/89001*G(12,2,2,r) +5046363708/9889*G(13,2,2,r) +193486010/341*G(14,2,2,r) +7038226032/14245*G(15,2,2,r) +853559307/2590*G(16,2,2,r) +78047478/481*G(17,2,2,r) +720309/13*G(18,2,2,r) +478800/41*G(19,2,2,r) +1140*G(20,2,2,r) R(20,16,r) = +4/55*G(0,2,2,r) +21468/168245*G(1,2,2,r) -24692/33649*G(2,2,2,r) -26056/4807*G(3,2,2,r) -836910/62491*G(4,2,2,r) +3429104/142025*G(5,2,2,r) +4051984/10925*G(6,2,2,r) +5227296/2755*G(7,2,2,r) +2941310216/443555*G(8,2,2,r) +2589685072/144739*G(9,2,2,r) +20119388718/516925*G(10,2,2,r) +51531883624/741675*G(11,2,2,r) +3036191704/29667*G(12,2,2,r) +1227093048/9889*G(13,2,2,r) +41852640/341*G(14,2,2,r) +1388331792/14245*G(15,2,2,r) +78463296/1295*G(16,2,2,r) +13641468/481*G(17,2,2,r) +121904/13*G(18,2,2,r) +79800/41*G(19,2,2,r) +190*G(20,2,2,r) R(20,18,r) = -9/110*G(0,2,2,r) -2526/8855*G(1,2,2,r) -361/1771*G(2,2,2,r) +912/253*G(3,2,2,r) +87210/3289*G(4,2,2,r) +886312/7475*G(5,2,2,r) +233852/575*G(6,2,2,r) +3813984/3335*G(7,2,2,r) +63245338/23345*G(8,2,2,r) +792065768/144739*G(9,2,2,r) +4893447416/516925*G(10,2,2,r) +10394506928/741675*G(11,2,2,r) +174800171/9889*G(12,2,2,r) +186245676/9889*G(13,2,2,r) +184110/11*G(14,2,2,r) +173505264/14245*G(15,2,2,r) +18305379/2590*G(16,2,2,r) +1511526/481*G(17,2,2,r) +13053/13*G(18,2,2,r) +8400/41*G(19,2,2,r) +20*G(20,2,2,r) R(20,20,r) = +1/11*G(0,2,2,r) +120/253*G(1,2,2,r) +475/253*G(2,2,2,r) +1596/253*G(3,2,2,r) +61047/3289*G(4,2,2,r) +72352/1495*G(5,2,2,r) +2584/23*G(6,2,2,r) +155040/667*G(7,2,2,r) +285532/667*G(8,2,2,r) +43400864/62031*G(9,2,2,r) +104433329/103385*G(10,2,2,r) +37975756/29667*G(11,2,2,r) +13961675/9889*G(12,2,2,r) +13255920/9889*G(13,2,2,r) +368220/341*G(14,2,2,r) +294576/407*G(15,2,2,r) +14535/37*G(16,2,2,r) +79800/481*G(17,2,2,r) +665/13*G(18,2,2,r) +420/41*G(19,2,2,r) +1*G(20,2,2,r) R(21,1,r) = +2/483*G(0,2,2,r) -8/161*G(1,2,2,r) +1116/3059*G(2,2,2,r) -2752/1311*G(3,2,2,r) +71700/7429*G(4,2,2,r) -1161072/37145*G(5,2,2,r) +3755752/170085*G(6,2,2,r) +833710592/1508087*G(7,2,2,r) -11245378716/2750041*G(8,2,2,r) +13847856880/1302651*G(9,2,2,r) +2586794600/62031*G(10,2,2,r) -1617822336/4495*G(11,2,2,r) -3238560520/8091*G(12,2,2,r) +6887244000/899*G(13,2,2,r) +284952891600/8029*G(14,2,2,r) +19998937088/259*G(15,2,2,r) +26407075596/259*G(16,2,2,r) +3246305040/37*G(17,2,2,r) +6121534760/123*G(18,2,2,r) +739024000/41*G(19,2,2,r) +162954792/43*G(20,2,2,r) +352716*G(21,2,2,r) R(21,3,r) = -2/161*G(0,2,2,r) +2157/17710*G(1,2,2,r) -20586/33649*G(2,2,2,r) +8130/4807*G(3,2,2,r) +81786/81719*G(4,2,2,r) -285069/7429*G(5,2,2,r) +1063392512/5386025*G(6,2,2,r) -2028283608/7540435*G(7,2,2,r) -7641889632/2750041*G(8,2,2,r) +7369189685/434217*G(9,2,2,r) +3257748/667*G(10,2,2,r) -289450668/775*G(11,2,2,r) +2120124604/29667*G(12,2,2,r) +82271703150/9889*G(13,2,2,r) +2939895550800/88319*G(14,2,2,r) +194937721056/2849*G(15,2,2,r) +113614478676/1295*G(16,2,2,r) +2747995821/37*G(17,2,2,r) +1711609300/41*G(18,2,2,r) +617001060/41*G(19,2,2,r) +135795660/43*G(20,2,2,r) +293930*G(21,2,2,r) R(21,5,r) = +10/483*G(0,2,2,r) -2951/17710*G(1,2,2,r) +16878/33649*G(2,2,2,r) +320230/562419*G(3,2,2,r) -1109698/96577*G(4,2,2,r) +3655179/96577*G(5,2,2,r) +357594944/5386025*G(6,2,2,r) -7199901096/7540435*G(7,2,2,r) +4399647360/2750041*G(8,2,2,r) +6594235505/434217*G(9,2,2,r) -1157996996/20677*G(10,2,2,r) -6517180644/22475*G(11,2,2,r) +240214962572/267003*G(12,2,2,r) +87905615350/9889*G(13,2,2,r) +2523036891600/88319*G(14,2,2,r) +13779604320/259*G(15,2,2,r) +1087915993956/16835*G(16,2,2,r) +25504108101/481*G(17,2,2,r) +15605777300/533*G(18,2,2,r) +428743740/41*G(19,2,2,r) +94012380/43*G(20,2,2,r) +203490*G(21,2,2,r) R(21,7,r) = -2/69*G(0,2,2,r) +233/1265*G(1,2,2,r) -768/4807*G(2,2,2,r) -65800/24453*G(3,2,2,r) +583072/55913*G(4,2,2,r) +2042145/96577*G(5,2,2,r) -1273486228/5386025*G(6,2,2,r) +48491436/1077205*G(7,2,2,r) +1729007994/392863*G(8,2,2,r) -240124885/62031*G(9,2,2,r) -9031763104/103385*G(10,2,2,r) -674261952/22475*G(11,2,2,r) +461321290976/267003*G(12,2,2,r) +83540965480/9889*G(13,2,2,r) +272754324000/12617*G(14,2,2,r) +14518910928/407*G(15,2,2,r) +96990520104/2405*G(16,2,2,r) +15239610288/481*G(17,2,2,r) +9090124400/533*G(18,2,2,r) +246358560/41*G(19,2,2,r) +53721360/43*G(20,2,2,r) +116280*G(21,2,2,r) R(21,9,r) = +6/161*G(0,2,2,r) -309/1771*G(1,2,2,r) -9696/33649*G(2,2,2,r) +645416/187473*G(3,2,2,r) +674304/1062347*G(4,2,2,r) -29474019/482885*G(5,2,2,r) +1528884/56695*G(6,2,2,r) +1662143580/1508087*G(7,2,2,r) -353852634/2750041*G(8,2,2,r) -3029450281/144739*G(9,2,2,r) -3791644064/103385*G(10,2,2,r) +273747136/899*G(11,2,2,r) +185266775200/89001*G(12,2,2,r) +66183530280/9889*G(13,2,2,r) +1226592407520/88319*G(14,2,2,r) +57452737872/2849*G(15,2,2,r) +70706728440/3367*G(16,2,2,r) +7529595120/481*G(17,2,2,r) +4349414640/533*G(18,2,2,r) +115814880/41*G(19,2,2,r) +25069968/43*G(20,2,2,r) +54264*G(21,2,2,r) R(21,11,r) = -22/483*G(0,2,2,r) +487/3542*G(1,2,2,r) +24114/33649*G(2,2,2,r) -1324982/562419*G(3,2,2,r) -13807754/1062347*G(4,2,2,r) +16023681/482885*G(5,2,2,r) +281612576/1077205*G(6,2,2,r) -335611680/1508087*G(7,2,2,r) -14331403824/2750041*G(8,2,2,r) -8617234769/868434*G(9,2,2,r) +6547822346/103385*G(10,2,2,r) +442201890/899*G(11,2,2,r) +473995065050/267003*G(12,2,2,r) +41928661705/9889*G(13,2,2,r) +645464215080/88319*G(14,2,2,r) +26658678792/2849*G(15,2,2,r) +30083816250/3367*G(16,2,2,r) +6043057065/962*G(17,2,2,r) +1681353890/533*G(18,2,2,r) +43827870/41*G(19,2,2,r) +9401238/43*G(20,2,2,r) +20349*G(21,2,2,r) R(21,13,r) = +26/483*G(0,2,2,r) -1297/17710*G(1,2,2,r) -33654/33649*G(2,2,2,r) -155930/562419*G(3,2,2,r) +1037198/62491*G(4,2,2,r) +230913/5681*G(5,2,2,r) -59180128/316825*G(6,2,2,r) -571882848/443555*G(7,2,2,r) -3608914224/2750041*G(8,2,2,r) +15601975675/868434*G(9,2,2,r) +539329726/4495*G(10,2,2,r) +9729075486/22475*G(11,2,2,r) +291734948882/267003*G(12,2,2,r) +20505013165/9889*G(13,2,2,r) +268144036200/88319*G(14,2,2,r) +9827540472/2849*G(15,2,2,r) +50815633266/16835*G(16,2,2,r) +1918894797/962*G(17,2,2,r) +512277050/533*G(18,2,2,r) +13030770/41*G(19,2,2,r) +2765070/43*G(20,2,2,r) +5985*G(21,2,2,r) R(21,15,r) = -10/161*G(0,2,2,r) -162/8855*G(1,2,2,r) +34092/33649*G(2,2,2,r) +212640/62491*G(3,2,2,r) -362508/62491*G(4,2,2,r) -454926/5681*G(5,2,2,r) -72799216/316825*G(6,2,2,r) +153859344/443555*G(7,2,2,r) +16356522120/2750041*G(8,2,2,r) +12886645915/434217*G(9,2,2,r) +2024590724/20677*G(10,2,2,r) +5470923952/22475*G(11,2,2,r) +14157108836/29667*G(12,2,2,r) +7424814600/9889*G(13,2,2,r) +84069124200/88319*G(14,2,2,r) +2755736040/2849*G(15,2,2,r) +13081750002/16835*G(16,2,2,r) +231833592/481*G(17,2,2,r) +118444100/533*G(18,2,2,r) +2932080/41*G(19,2,2,r) +614460/43*G(20,2,2,r) +1330*G(21,2,2,r) R(21,17,r) = +34/483*G(0,2,2,r) +1214/8855*G(1,2,2,r) -1116/1771*G(2,2,2,r) -17120/3289*G(3,2,2,r) -4428/299*G(4,2,2,r) +3366/299*G(5,2,2,r) +16052624/50025*G(6,2,2,r) +42146128/23345*G(7,2,2,r) +976928664/144739*G(8,2,2,r) +25319193185/1302651*G(9,2,2,r) +14059881212/310155*G(10,2,2,r) +1965736656/22475*G(11,2,2,r) +4175871908/29667*G(12,2,2,r) +1869666120/9889*G(13,2,2,r) +18622823400/88319*G(14,2,2,r) +50033992/259*G(15,2,2,r) +2406098706/16835*G(16,2,2,r) +40023576/481*G(17,2,2,r) +58597900/1599*G(18,2,2,r) +469520/41*G(19,2,2,r) +97020/43*G(20,2,2,r) +210*G(21,2,2,r) R(21,19,r) = -38/483*G(0,2,2,r) -1003/3542*G(1,2,2,r) -486/1771*G(2,2,2,r) +10222/3289*G(3,2,2,r) +81054/3289*G(4,2,2,r) +171513/1495*G(5,2,2,r) +4087888/10005*G(6,2,2,r) +242896/203*G(7,2,2,r) +429484056/144739*G(8,2,2,r) +16455708841/2605302*G(9,2,2,r) +3599559158/310155*G(10,2,2,r) +82812678/4495*G(11,2,2,r) +747547970/29667*G(12,2,2,r) +291906405/9889*G(13,2,2,r) +2591532360/88319*G(14,2,2,r) +69579368/2849*G(15,2,2,r) +56234946/3367*G(16,2,2,r) +8788545/962*G(17,2,2,r) +6140230/1599*G(18,2,2,r) +47690/41*G(19,2,2,r) +9702/43*G(20,2,2,r) +21*G(21,2,2,r) R(21,21,r) = +2/23*G(0,2,2,r) +21/46*G(1,2,2,r) +42/23*G(2,2,2,r) +1862/299*G(3,2,2,r) +5586/299*G(4,2,2,r) +74613/1495*G(5,2,2,r) +397936/3335*G(6,2,2,r) +170544/667*G(7,2,2,r) +10147368/20677*G(8,2,2,r) +104433329/124062*G(9,2,2,r) +132915146/103385*G(10,2,2,r) +7818538/4495*G(11,2,2,r) +5584670/2697*G(12,2,2,r) +1933155/899*G(13,2,2,r) +2209320/1147*G(14,2,2,r) +54264/37*G(15,2,2,r) +447678/481*G(16,2,2,r) +460845/962*G(17,2,2,r) +102410/533*G(18,2,2,r) +2310/41*G(19,2,2,r) +462/43*G(20,2,2,r) +1*G(21,2,2,r) R(22,0,r) = +12/4025*G(1,2,2,r) -48/805*G(2,2,2,r) +2680/3933*G(3,2,2,r) -2512/437*G(4,2,2,r) +8240232/215441*G(5,2,2,r) -1063526464/5386025*G(6,2,2,r) +1211242032/1757545*G(7,2,2,r) -46881120/94829*G(8,2,2,r) -1728605736/144739*G(9,2,2,r) +1483003808/20677*G(10,2,2,r) -108346576/4495*G(11,2,2,r) -386378720/261*G(12,2,2,r) +50180348400/33263*G(13,2,2,r) +39902204160/1147*G(14,2,2,r) +31767851040/259*G(15,2,2,r) +299470488768/1295*G(16,2,2,r) +418426207848/1517*G(17,2,2,r) +8979141600/41*G(18,2,2,r) +204779855280/1763*G(19,2,2,r) +1707145440/43*G(20,2,2,r) +118982864/15*G(21,2,2,r) +705432*G(22,2,2,r) R(22,2,r) = +1/132*G(0,2,2,r) -3629/44275*G(1,2,2,r) +8907/17710*G(2,2,2,r) -282836/129789*G(3,2,2,r) +171187/28842*G(4,2,2,r) +2127426/1077205*G(5,2,2,r) -2183706161/16158075*G(6,2,2,r) +27471008864/33393355*G(7,2,2,r) -10936471533/5500082*G(8,2,2,r) -9280010246/1302651*G(9,2,2,r) +22900373353/310155*G(10,2,2,r) -4581469672/49445*G(11,2,2,r) -374050808495/267003*G(12,2,2,r) +853004630660/365893*G(13,2,2,r) +444288121290/12617*G(14,2,2,r) +336077489632/2849*G(15,2,2,r) +563272216413/2590*G(16,2,2,r) +388796023134/1517*G(17,2,2,r) +24858640405/123*G(18,2,2,r) +188245704920/1763*G(19,2,2,r) +1566147219/43*G(20,2,2,r) +327202876/45*G(21,2,2,r) +646646*G(22,2,2,r) R(22,4,r) = -1/66*G(0,2,2,r) +1214/8855*G(1,2,2,r) -13218/23023*G(2,2,2,r) +1385260/1687257*G(3,2,2,r) +1107440/187473*G(4,2,2,r) -643831692/14003665*G(5,2,2,r) +75502126/646323*G(6,2,2,r) +121331008/351509*G(7,2,2,r) -10320229977/2750041*G(8,2,2,r) +8775222436/1302651*G(9,2,2,r) +17695907944/310155*G(10,2,2,r) -12416503112/49445*G(11,2,2,r) -9386174980/9207*G(12,2,2,r) +1636364539880/365893*G(13,2,2,r) +446966155260/12617*G(14,2,2,r) +3852467853088/37037*G(15,2,2,r) +606796791351/3367*G(16,2,2,r) +4046297777100/19721*G(17,2,2,r) +253576763740/1599*G(18,2,2,r) +146029398200/1763*G(19,2,2,r) +1207645320/43*G(20,2,2,r) +50338904/9*G(21,2,2,r) +497420*G(22,2,2,r) R(22,6,r) = +1/44*G(0,2,2,r) -213/1265*G(1,2,2,r) +2487/6578*G(2,2,2,r) +256340/187473*G(3,2,2,r) -1489845/124982*G(4,2,2,r) +262787238/14003665*G(5,2,2,r) +33187875/215441*G(6,2,2,r) -5418288288/6678671*G(7,2,2,r) -651028077/785726*G(8,2,2,r) +1074926174/62031*G(9,2,2,r) -22205183/3565*G(10,2,2,r) -17098644472/49445*G(11,2,2,r) -4374320405/29667*G(12,2,2,r) +2525466173580/365893*G(13,2,2,r) +418838361390/12617*G(14,2,2,r) +435007914144/5291*G(15,2,2,r) +125265429441/962*G(16,2,2,r) +2773362157650/19721*G(17,2,2,r) +56127527505/533*G(18,2,2,r) +95188552200/1763*G(19,2,2,r) +779468445/43*G(20,2,2,r) +3595636*G(21,2,2,r) +319770*G(22,2,2,r) R(22,8,r) = -1/33*G(0,2,2,r) +1112/6325*G(1,2,2,r) -324/16445*G(2,2,2,r) -1669024/562419*G(3,2,2,r) +456484/62491*G(4,2,2,r) +27152496/737035*G(5,2,2,r) -1057597198/5386025*G(6,2,2,r) -12945463944/33393355*G(7,2,2,r) +1573150635/392863*G(8,2,2,r) +1059452800/186093*G(9,2,2,r) -1012259248/13485*G(10,2,2,r) -50642294976/247225*G(11,2,2,r) +29980389712/29667*G(12,2,2,r) +2995974616320/365893*G(13,2,2,r) +343998284400/12617*G(14,2,2,r) +299474747200/5291*G(15,2,2,r) +194183584464/2405*G(16,2,2,r) +1610506790928/19721*G(17,2,2,r) +31279216640/533*G(18,2,2,r) +51747235680/1763*G(19,2,2,r) +418049856/43*G(20,2,2,r) +28765088/15*G(21,2,2,r) +170544*G(22,2,2,r) R(22,10,r) = +5/132*G(0,2,2,r) -7057/44275*G(1,2,2,r) -91197/230230*G(2,2,2,r) +1782260/562419*G(3,2,2,r) +510677/124982*G(4,2,2,r) -160893054/2800733*G(5,2,2,r) -305294731/5386025*G(6,2,2,r) +34075276032/33393355*G(7,2,2,r) +18103885875/11000164*G(8,2,2,r) -22027750475/1302651*G(9,2,2,r) -7939165091/124062*G(10,2,2,r) +34830967548/247225*G(11,2,2,r) +108939985973/59334*G(12,2,2,r) +2731843557450/365893*G(13,2,2,r) +236647215225/12617*G(14,2,2,r) +1219926684400/37037*G(15,2,2,r) +2835795720099/67340*G(16,2,2,r) +780617765241/19721*G(17,2,2,r) +28894312225/1066*G(18,2,2,r) +23190670020/1763*G(19,2,2,r) +368418645/86*G(20,2,2,r) +12584726/15*G(21,2,2,r) +74613*G(22,2,2,r) R(22,12,r) = -1/22*G(0,2,2,r) +5274/44275*G(1,2,2,r) +88002/115115*G(2,2,2,r) -331468/187473*G(3,2,2,r) -884256/62491*G(4,2,2,r) +2909340/164749*G(5,2,2,r) +85266006/316825*G(6,2,2,r) +262882368/1964315*G(7,2,2,r) -25021537839/5500082*G(8,2,2,r) -6581370310/434217*G(9,2,2,r) +3161651636/103385*G(10,2,2,r) +105548893684/247225*G(11,2,2,r) +55441519042/29667*G(12,2,2,r) +61394496660/11803*G(13,2,2,r) +131592461850/12617*G(14,2,2,r) +582052671888/37037*G(15,2,2,r) +606988730871/33670*G(16,2,2,r) +309448477278/19721*G(17,2,2,r) +5431259250/533*G(18,2,2,r) +8422738380/1763*G(19,2,2,r) +65581236/43*G(20,2,2,r) +1480556/5*G(21,2,2,r) +26334*G(22,2,2,r) R(22,14,r) = +7/132*G(0,2,2,r) -487/8855*G(1,2,2,r) -45147/46046*G(2,2,2,r) -1401580/1687257*G(3,2,2,r) +5602985/374946*G(4,2,2,r) +41176758/823745*G(5,2,2,r) -4633559/38019*G(6,2,2,r) -497869568/392863*G(7,2,2,r) -27986345931/11000164*G(8,2,2,r) +223084999/18879*G(9,2,2,r) +22388214277/206770*G(10,2,2,r) +22219280772/49445*G(11,2,2,r) +21966464065/17226*G(12,2,2,r) +32133069010/11803*G(13,2,2,r) +57140939835/12617*G(14,2,2,r) +220051977456/37037*G(15,2,2,r) +82710193653/13468*G(16,2,2,r) +97548869475/19721*G(17,2,2,r) +9714455185/3198*G(18,2,2,r) +2417713900/1763*G(19,2,2,r) +36805755/86*G(20,2,2,r) +740278/9*G(21,2,2,r) +7315*G(22,2,2,r) R(22,16,r) = -2/33*G(0,2,2,r) -292/8855*G(1,2,2,r) +21624/23023*G(2,2,2,r) +13960/3861*G(3,2,2,r) -30440/9867*G(4,2,2,r) -3197208/43355*G(5,2,2,r) -520268/2001*G(6,2,2,r) +1342048/20677*G(7,2,2,r) +716529549/144739*G(8,2,2,r) +12312952508/434217*G(9,2,2,r) +10607950496/103385*G(10,2,2,r) +13748567352/49445*G(11,2,2,r) +159305357120/267003*G(12,2,2,r) +379430076760/365893*G(13,2,2,r) +18567357840/12617*G(14,2,2,r) +63093047376/37037*G(15,2,2,r) +5372182512/3367*G(16,2,2,r) +23479821900/19721*G(17,2,2,r) +1104141680/1599*G(18,2,2,r) +527955400/1763*G(19,2,2,r) +3919440/43*G(20,2,2,r) +155848/9*G(21,2,2,r) +1540*G(22,2,2,r) R(22,18,r) = +3/44*G(0,2,2,r) +6411/44275*G(1,2,2,r) -123369/230230*G(2,2,2,r) -147044/29601*G(3,2,2,r) -104177/6578*G(4,2,2,r) +798/43355*G(5,2,2,r) +4546871/16675*G(6,2,2,r) +175536288/103385*G(7,2,2,r) +3920293959/578956*G(8,2,2,r) +2996641867/144739*G(9,2,2,r) +2126402993/41354*G(10,2,2,r) +26283371764/247225*G(11,2,2,r) +32922188117/178002*G(12,2,2,r) +99357723150/365893*G(13,2,2,r) +4235106555/12617*G(14,2,2,r) +12848025264/37037*G(15,2,2,r) +19945040373/67340*G(16,2,2,r) +4047111207/19721*G(17,2,2,r) +119803455/1066*G(18,2,2,r) +82417020/1763*G(19,2,2,r) +1191183/86*G(20,2,2,r) +38962/15*G(21,2,2,r) +231*G(22,2,2,r) R(22,20,r) = -5/66*G(0,2,2,r) -1774/6325*G(1,2,2,r) -5502/16445*G(2,2,2,r) +236180/88803*G(3,2,2,r) +225568/9867*G(4,2,2,r) +959196/8671*G(5,2,2,r) +20407786/50025*G(6,2,2,r) +128176736/103385*G(7,2,2,r) +132525285/41354*G(8,2,2,r) +1330612066/186093*G(9,2,2,r) +860039180/62031*G(10,2,2,r) +5787951988/247225*G(11,2,2,r) +9180080546/267003*G(12,2,2,r) +16002227500/365893*G(13,2,2,r) +603812970/12617*G(14,2,2,r) +235996720/5291*G(15,2,2,r) +167967429/4810*G(16,2,2,r) +444304854/19721*G(17,2,2,r) +18639950/1599*G(18,2,2,r) +8192380/1763*G(19,2,2,r) +57540/43*G(20,2,2,r) +11132/45*G(21,2,2,r) +22*G(22,2,2,r) R(22,22,r) = +1/12*G(0,2,2,r) +11/25*G(1,2,2,r) +231/130*G(2,2,2,r) +2156/351*G(3,2,2,r) +1463/78*G(4,2,2,r) +96558/1885*G(5,2,2,r) +273581/2175*G(6,2,2,r) +1250656/4495*G(7,2,2,r) +1993233/3596*G(8,2,2,r) +8033333/8091*G(9,2,2,r) +43001959/26970*G(10,2,2,r) +51378964/22475*G(11,2,2,r) +141292151/48546*G(12,2,2,r) +108686270/33263*G(13,2,2,r) +3677355/1147*G(14,2,2,r) +1307504/481*G(15,2,2,r) +18877089/9620*G(16,2,2,r) +23318757/19721*G(17,2,2,r) +1850695/3198*G(18,2,2,r) +389620/1763*G(19,2,2,r) +5313/86*G(20,2,2,r) +506/45*G(21,2,2,r) +1*G(22,2,2,r) Zernike polynomials R(n,m,r) in terms of Jacobi Polynomials G(n,m+1,m+1,r): R(0,0,r) = +1*G(0,1,1,r) R(1,1,r) = +2/3*G(0,2,2,r) +1*G(1,2,2,r) R(2,0,r) = -1/3*G(0,1,1,r) +2*G(1,1,1,r) +2*G(2,1,1,r) R(2,2,r) = +3/5*G(0,3,3,r) +4/3*G(1,3,3,r) +1*G(2,3,3,r) R(3,1,r) = -2/15*G(0,2,2,r) +8/5*G(1,2,2,r) +36/7*G(2,2,2,r) +3*G(3,2,2,r) R(3,3,r) = +4/7*G(0,4,4,r) +45/28*G(1,4,4,r) +2*G(2,4,4,r) +1*G(3,4,4,r) R(4,0,r) = +1/5*G(0,1,1,r) -6/5*G(1,1,1,r) +30/7*G(2,1,1,r) +12*G(3,1,1,r) +6*G(4,1,1,r) R(4,2,r) = -3/35*G(0,3,3,r) +12/7*G(1,3,3,r) +7*G(2,3,3,r) +48/5*G(3,3,3,r) +4*G(4,3,3,r) R(4,4,r) = +5/9*G(0,5,5,r) +28/15*G(1,5,5,r) +168/55*G(2,5,5,r) +8/3*G(3,5,5,r) +1*G(4,5,5,r) R(5,1,r) = +2/35*G(0,2,2,r) -24/35*G(1,2,2,r) +68/21*G(2,2,2,r) +64/3*G(3,2,2,r) +300/11*G(4,2,2,r) +10*G(5,2,2,r) R(5,3,r) = -4/63*G(0,4,4,r) +40/21*G(1,4,4,r) +296/33*G(2,4,4,r) +568/33*G(3,4,4,r) +200/13*G(4,4,4,r) +5*G(5,4,4,r) R(5,5,r) = +6/11*G(0,6,6,r) +70/33*G(1,6,6,r) +600/143*G(2,6,6,r) +450/91*G(3,6,6,r) +10/3*G(4,6,6,r) +1*G(5,6,6,r) R(6,0,r) = -1/7*G(0,1,1,r) +6/7*G(1,1,1,r) -26/7*G(2,1,1,r) +20/3*G(3,1,1,r) +570/11*G(4,1,1,r) +60*G(5,1,1,r) +20*G(6,1,1,r) R(6,2,r) = +1/35*G(0,3,3,r) -4/7*G(1,3,3,r) +41/11*G(2,3,3,r) +312/11*G(3,3,3,r) +790/13*G(4,3,3,r) +360/7*G(5,3,3,r) +15*G(6,3,3,r) R(6,4,r) = -5/99*G(0,5,5,r) +70/33*G(1,5,5,r) +1596/143*G(2,5,5,r) +7160/273*G(3,5,5,r) +235/7*G(4,5,5,r) +45/2*G(5,5,5,r) +6*G(6,5,5,r) R(6,6,r) = +7/13*G(0,7,7,r) +216/91*G(1,7,7,r) +495/91*G(2,7,7,r) +55/7*G(3,7,7,r) +495/68*G(4,7,7,r) +4*G(5,7,7,r) +1*G(6,7,7,r) R(7,1,r) = -2/63*G(0,2,2,r) +8/21*G(1,2,2,r) -180/77*G(2,2,2,r) +320/99*G(3,2,2,r) +10900/143*G(4,2,2,r) +2160/13*G(5,2,2,r) +392/3*G(6,2,2,r) +35*G(7,2,2,r) R(7,3,r) = +4/231*G(0,4,4,r) -40/77*G(1,4,4,r) +648/143*G(2,4,4,r) +480/13*G(3,4,4,r) +1320/13*G(4,4,4,r) +1083/8*G(5,4,4,r) +1470/17*G(6,4,4,r) +21*G(7,4,4,r) R(7,5,r) = -6/143*G(0,6,6,r) +336/143*G(1,6,6,r) +1944/143*G(2,6,6,r) +1035/28*G(3,6,6,r) +2015/34*G(4,6,6,r) +976/17*G(5,6,6,r) +588/19*G(6,6,6,r) +7*G(7,6,6,r) R(7,7,r) = +8/15*G(0,8,8,r) +21/8*G(1,8,8,r) +231/34*G(2,8,8,r) +7007/612*G(3,8,8,r) +12740/969*G(4,8,8,r) +1911/190*G(5,8,8,r) +14/3*G(6,8,8,r) +1*G(7,8,8,r) R(8,0,r) = +1/9*G(0,1,1,r) -2/3*G(1,1,1,r) +710/231*G(2,1,1,r) -940/99*G(3,1,1,r) -430/143*G(4,1,1,r) +2380/13*G(5,1,1,r) +1148/3*G(6,1,1,r) +280*G(7,1,1,r) +70*G(8,1,1,r) R(8,2,r) = -1/77*G(0,3,3,r) +20/77*G(1,3,3,r) -315/143*G(2,3,3,r) +600/143*G(3,3,3,r) +1270/13*G(4,3,3,r) +312*G(5,3,3,r) +7035/17*G(6,3,3,r) +2240/9*G(7,3,3,r) +56*G(8,3,3,r) R(8,4,r) = +5/429*G(0,5,5,r) -70/143*G(1,5,5,r) +3948/715*G(2,5,5,r) +616/13*G(3,5,5,r) +2595/17*G(4,5,5,r) +27055/102*G(5,5,5,r) +14854/57*G(6,5,5,r) +672/5*G(7,5,5,r) +28*G(8,5,5,r) R(8,6,r) = -7/195*G(0,7,7,r) +168/65*G(1,7,7,r) +3597/221*G(2,7,7,r) +7601/153*G(3,7,7,r) +363055/3876*G(4,7,7,r) +32788/285*G(5,7,7,r) +1351/15*G(6,7,7,r) +448/11*G(7,7,7,r) +8*G(8,7,7,r) R(8,8,r) = +9/17*G(0,9,9,r) +440/153*G(1,9,9,r) +8008/969*G(2,9,9,r) +5096/323*G(3,9,9,r) +3640/171*G(4,9,9,r) +224/11*G(5,9,9,r) +3360/253*G(6,9,9,r) +16/3*G(7,9,9,r) +1*G(8,9,9,r) R(9,1,r) = +2/99*G(0,2,2,r) -8/33*G(1,2,2,r) +1620/1001*G(2,2,2,r) -7360/1287*G(3,2,2,r) -1988/143*G(4,2,2,r) +3024/13*G(5,2,2,r) +41944/51*G(6,2,2,r) +17920/17*G(7,2,2,r) +11340/19*G(8,2,2,r) +126*G(9,2,2,r) R(9,3,r) = -20/3003*G(0,4,4,r) +200/1001*G(1,4,4,r) -1608/715*G(2,4,4,r) +864/143*G(3,4,4,r) +28056/221*G(4,4,4,r) +8400/17*G(5,4,4,r) +294000/323*G(6,4,4,r) +83832/95*G(7,4,4,r) +432*G(8,4,4,r) +84*G(9,4,4,r) R(9,5,r) = +6/715*G(0,6,6,r) -336/715*G(1,6,6,r) +16200/2431*G(2,6,6,r) +13248/221*G(3,6,6,r) +70042/323*G(4,6,6,r) +728147/1615*G(5,6,6,r) +55104/95*G(6,6,6,r) +5000/11*G(7,6,6,r) +4536/23*G(8,6,6,r) +36*G(9,6,6,r) R(9,7,r) = -8/255*G(0,8,8,r) +48/17*G(1,8,8,r) +6204/323*G(2,8,8,r) +938938/14535*G(3,8,8,r) +133952/969*G(4,8,8,r) +210756/1045*G(5,8,8,r) +153104/759*G(6,8,8,r) +3056/23*G(7,8,8,r) +1296/25*G(8,8,8,r) +9*G(9,8,8,r) R(9,9,r) = +10/19*G(0,10,10,r) +297/95*G(1,10,10,r) +936/95*G(2,10,10,r) +4368/209*G(3,10,10,r) +154224/4807*G(4,10,10,r) +9180/253*G(5,10,10,r) +17136/575*G(6,10,10,r) +5508/325*G(7,10,10,r) +6*G(8,10,10,r) +1*G(9,10,10,r) R(10,0,r) = -1/11*G(0,1,1,r) +6/11*G(1,1,1,r) -370/143*G(2,1,1,r) +4060/429*G(3,1,1,r) -210/13*G(4,1,1,r) -84*G(5,1,1,r) +8932/17*G(6,1,1,r) +32760/17*G(7,1,1,r) +44730/19*G(8,1,1,r) +1260*G(9,1,1,r) +252*G(10,1,1,r) R(10,2,r) = +1/143*G(0,3,3,r) -20/143*G(1,3,3,r) +185/143*G(2,3,3,r) -840/143*G(3,3,3,r) -3010/221*G(4,3,3,r) +4824/17*G(5,3,3,r) +446565/323*G(6,3,3,r) +49840/19*G(7,3,3,r) +2466*G(8,3,3,r) +12600/11*G(9,3,3,r) +210*G(10,3,3,r) R(10,4,r) = -5/1287*G(0,5,5,r) +70/429*G(1,5,5,r) -2604/1105*G(2,5,5,r) +5656/663*G(3,5,5,r) +53405/323*G(4,5,5,r) +235830/323*G(5,5,5,r) +31528/19*G(6,5,5,r) +120672/55*G(7,5,5,r) +427644/253*G(8,5,5,r) +700*G(9,5,5,r) +120*G(10,5,5,r) R(10,6,r) = +7/1105*G(0,7,7,r) -504/1105*G(1,7,7,r) +33363/4199*G(2,7,7,r) +24156/323*G(3,7,7,r) +95865/323*G(4,7,7,r) +737296/1045*G(5,7,7,r) +1387316/1265*G(6,7,7,r) +285264/253*G(7,7,7,r) +738*G(8,7,7,r) +3600/13*G(9,7,7,r) +45*G(10,7,7,r) R(10,8,r) = -9/323*G(0,9,9,r) +990/323*G(1,9,9,r) +50622/2261*G(2,9,9,r) +291096/3553*G(3,9,9,r) +935480/4807*G(4,9,9,r) +82152/253*G(5,9,9,r) +98280/253*G(6,9,9,r) +4272/13*G(7,9,9,r) +2433/13*G(8,9,9,r) +450/7*G(9,9,9,r) +10*G(10,9,9,r) R(10,10,r) = +11/21*G(0,11,11,r) +260/77*G(1,11,11,r) +2925/253*G(2,11,11,r) +6800/253*G(3,11,11,r) +11628/253*G(4,11,11,r) +976752/16445*G(5,11,11,r) +2261/39*G(6,11,11,r) +3800/91*G(7,11,11,r) +4275/203*G(8,11,11,r) +20/3*G(9,11,11,r) +1*G(10,11,11,r) R(11,1,r) = -2/143*G(0,2,2,r) +24/143*G(1,2,2,r) -500/429*G(2,2,2,r) +2240/429*G(3,2,2,r) -14700/2431*G(4,2,2,r) -24976/221*G(5,2,2,r) +182280/323*G(6,2,2,r) +1128960/323*G(7,2,2,r) +126180/19*G(8,2,2,r) +6000*G(9,2,2,r) +60984/23*G(10,2,2,r) +462*G(11,2,2,r) R(11,3,r) = +4/1287*G(0,4,4,r) -40/429*G(1,4,4,r) +8344/7293*G(2,4,4,r) -48160/7293*G(3,4,4,r) -51080/4199*G(4,4,4,r) +117712/323*G(5,4,4,r) +39760/19*G(6,4,4,r) +97920/19*G(7,4,4,r) +158040/23*G(8,4,4,r) +236635/46*G(9,4,4,r) +10164/5*G(10,4,4,r) +330*G(11,4,4,r) R(11,5,r) = -6/2431*G(0,6,6,r) +336/2431*G(1,6,6,r) -8856/3553*G(2,6,6,r) +2880/247*G(3,6,6,r) +207530/969*G(4,6,6,r) +334880/323*G(5,6,6,r) +1194480/437*G(6,6,6,r) +1131576/253*G(7,6,6,r) +107100/23*G(8,6,6,r) +38880/13*G(9,6,6,r) +9680/9*G(10,6,6,r) +165*G(11,6,6,r) R(11,7,r) = +8/1615*G(0,8,8,r) -144/323*G(1,8,8,r) +21164/2261*G(2,8,8,r) +29744/323*G(3,8,8,r) +2935920/7429*G(4,8,8,r) +25123644/24035*G(5,8,8,r) +474432/253*G(6,8,8,r) +700344/299*G(7,8,8,r) +130864/65*G(8,8,8,r) +47645/42*G(9,8,8,r) +10890/29*G(10,8,8,r) +55*G(11,8,8,r) R(11,9,r) = -10/399*G(0,10,10,r) +440/133*G(1,10,10,r) +11284/437*G(2,10,10,r) +489710/4807*G(3,10,10,r) +1271736/4807*G(4,10,10,r) +1620576/3289*G(5,10,10,r) +3040688/4485*G(6,10,10,r) +313718/455*G(7,10,10,r) +102770/203*G(8,10,10,r) +22120/87*G(9,10,10,r) +2420/31*G(10,10,10,r) +11*G(11,10,10,r) R(11,11,r) = +12/23*G(0,12,12,r) +1001/276*G(1,12,12,r) +308/23*G(2,12,12,r) +10098/299*G(3,12,12,r) +56848/897*G(4,12,12,r) +273581/2990*G(5,12,12,r) +193116/1885*G(6,12,12,r) +22990/261*G(7,12,12,r) +50820/899*G(8,12,12,r) +12705/496*G(9,12,12,r) +22/3*G(10,12,12,r) +1*G(11,12,12,r) R(12,0,r) = +1/13*G(0,1,1,r) -6/13*G(1,1,1,r) +318/143*G(2,1,1,r) -1260/143*G(3,1,1,r) +56490/2431*G(4,1,1,r) +2268/221*G(5,1,1,r) -144564/323*G(6,1,1,r) +344232/323*G(7,1,1,r) +154890/19*G(8,1,1,r) +15180*G(9,1,1,r) +302148/23*G(10,1,1,r) +5544*G(11,1,1,r) +924*G(12,1,1,r) R(12,2,r) = -3/715*G(0,3,3,r) +12/143*G(1,3,3,r) -1967/2431*G(2,3,3,r) +11256/2431*G(3,3,3,r) -31990/4199*G(4,3,3,r) -192024/1615*G(5,3,3,r) +204813/323*G(6,3,3,r) +5392*G(7,3,3,r) +325854/23*G(8,3,3,r) +430920/23*G(9,3,3,r) +338646/25*G(10,3,3,r) +66528/13*G(11,3,3,r) +792*G(12,3,3,r) R(12,4,r) = +35/21879*G(0,5,5,r) -490/7293*G(1,5,5,r) +48804/46189*G(2,5,5,r) -95480/12597*G(3,5,5,r) -22045/2261*G(4,5,5,r) +8130/17*G(5,5,5,r) +1325912/437*G(6,5,5,r) +204624/23*G(7,5,5,r) +348390/23*G(8,5,5,r) +204820/13*G(9,5,5,r) +128040/13*G(10,5,5,r) +23760/7*G(11,5,5,r) +495*G(12,5,5,r) R(12,6,r) = -7/4199*G(0,7,7,r) +504/4199*G(1,7,7,r) -77715/29393*G(2,7,7,r) +34980/2261*G(3,7,7,r) +2042535/7429*G(4,7,7,r) +625680/437*G(5,7,7,r) +486108/115*G(6,7,7,r) +26618256/3289*G(7,7,7,r) +135690/13*G(8,7,7,r) +189200/21*G(9,7,7,r) +1010295/203*G(10,7,7,r) +1584*G(11,7,7,r) +220*G(12,7,7,r) R(12,8,r) = +9/2261*G(0,9,9,r) -990/2261*G(1,9,9,r) +567138/52003*G(2,9,9,r) +832260/7429*G(3,9,9,r) +225004/437*G(4,9,9,r) +24480936/16445*G(5,9,9,r) +9851016/3289*G(6,9,9,r) +152016/35*G(7,9,9,r) +12011955/2639*G(8,9,9,r) +684090/203*G(9,9,9,r) +51766/31*G(10,9,9,r) +495*G(11,9,9,r) +66*G(12,9,9,r) R(12,10,r) = -11/483*G(0,11,11,r) +572/161*G(1,11,11,r) +3393/115*G(2,11,11,r) +37264/299*G(3,11,11,r) +104652/299*G(4,11,11,r) +46512/65*G(5,11,11,r) +6242621/5655*G(6,11,11,r) +3422584/2639*G(7,11,11,r) +7232445/6293*G(8,11,11,r) +69410/93*G(9,11,11,r) +671/2*G(10,11,11,r) +1584/17*G(11,11,11,r) +12*G(12,11,11,r) R(12,12,r) = +13/25*G(0,13,13,r) +252/65*G(1,13,13,r) +2992/195*G(2,13,13,r) +56848/1365*G(3,13,13,r) +31977/377*G(4,13,13,r) +1269048/9425*G(5,13,13,r) +5922224/35061*G(6,13,13,r) +150282/899*G(7,13,13,r) +15939/124*G(8,13,13,r) +1265/17*G(9,13,13,r) +18216/595*G(10,13,13,r) +8*G(11,13,13,r) +1*G(12,13,13,r) R(13,1,r) = +2/195*G(0,2,2,r) -8/65*G(1,2,2,r) +2124/2431*G(2,2,2,r) -31808/7293*G(3,2,2,r) +539700/46189*G(4,2,2,r) +722736/20995*G(5,2,2,r) -803144/1615*G(6,2,2,r) +250368/323*G(7,2,2,r) +5641812/437*G(8,2,2,r) +814000/23*G(9,2,2,r) +26365416/575*G(10,2,2,r) +798336/25*G(11,2,2,r) +104104/9*G(12,2,2,r) +1716*G(13,2,2,r) R(13,3,r) = -4/2431*G(0,4,4,r) +120/2431*G(1,4,4,r) -29176/46189*G(2,4,4,r) +1120/247*G(3,4,4,r) -312840/29393*G(4,4,4,r) -2448/19*G(5,4,4,r) +5909520/7429*G(6,4,4,r) +3420288/437*G(7,4,4,r) +2948616/115*G(8,4,4,r) +1031184/23*G(9,4,4,r) +230384/5*G(10,4,4,r) +195360/7*G(11,4,4,r) +267696/29*G(12,4,4,r) +1287*G(13,4,4,r) R(13,5,r) = +42/46189*G(0,6,6,r) -2352/46189*G(1,6,6,r) +24840/24871*G(2,6,6,r) -256320/29393*G(3,6,6,r) -45290/7429*G(4,6,6,r) +4686240/7429*G(5,6,6,r) +9368208/2185*G(6,6,6,r) +327936/23*G(7,6,6,r) +666204/23*G(8,6,6,r) +3473800/91*G(9,6,6,r) +6650160/203*G(10,6,6,r) +511434/29*G(11,6,6,r) +167310/31*G(12,6,6,r) +715*G(13,6,6,r) R(13,7,r) = -8/6783*G(0,8,8,r) +240/2261*G(1,8,8,r) -8580/3059*G(2,8,8,r) +148720/7429*G(3,8,8,r) +2595216/7429*G(4,8,8,r) +4226976/2185*G(5,8,8,r) +431728/69*G(6,8,8,r) +28339952/2093*G(7,8,8,r) +270836016/13195*G(8,8,8,r) +40110785/1827*G(9,8,8,r) +14598408/899*G(10,8,8,r) +488895/62*G(11,8,8,r) +6760/3*G(12,8,8,r) +286*G(13,8,8,r) R(13,9,r) = +10/3059*G(0,10,10,r) -1320/3059*G(1,10,10,r) +137436/10925*G(2,10,10,r) +294528/2185*G(3,10,10,r) +287912/437*G(4,10,10,r) +4304808/2093*G(5,10,10,r) +197379248/43355*G(6,10,10,r) +491097156/65975*G(7,10,10,r) +57225102/6293*G(8,10,10,r) +29590495/3596*G(9,10,10,r) +166155/31*G(10,10,10,r) +40344/17*G(11,10,10,r) +22308/35*G(12,10,10,r) +78*G(13,10,10,r) R(13,11,r) = -12/575*G(0,12,12,r) +2184/575*G(1,12,12,r) +11536/345*G(2,12,12,r) +1573792/10465*G(3,12,12,r) +82486448/182091*G(4,12,12,r) +217731393/216775*G(5,12,12,r) +498680688/292175*G(6,12,12,r) +6085453/2697*G(7,12,12,r) +67221/29*G(8,12,12,r) +1920765/1054*G(9,12,12,r) +631752/595*G(10,12,12,r) +15128/35*G(11,12,12,r) +4056/37*G(12,12,12,r) +13*G(13,12,12,r) R(13,13,r) = +14/27*G(0,14,14,r) +260/63*G(1,14,14,r) +3536/203*G(2,14,14,r) +92378/1827*G(3,14,14,r) +298870/2697*G(4,14,14,r) +687401/3596*G(5,14,14,r) +2137850/8091*G(6,14,14,r) +4489485/15283*G(7,14,14,r) +1924065/7378*G(8,14,14,r) +194350/1071*G(9,14,14,r) +74360/777*G(10,14,14,r) +25350/703*G(11,14,14,r) +26/3*G(12,14,14,r) +1*G(13,14,14,r) R(14,0,r) = -1/15*G(0,1,1,r) +2/5*G(1,1,1,r) -430/221*G(2,1,1,r) +5348/663*G(3,1,1,r) -1176378/46189*G(4,1,1,r) +51492/1615*G(5,1,1,r) +401548/1615*G(6,1,1,r) -531960/323*G(7,1,1,r) +101838/437*G(8,1,1,r) +673156/23*G(9,1,1,r) +46956756/575*G(10,1,1,r) +2570568/25*G(11,1,1,r) +620620/9*G(12,1,1,r) +24024*G(13,1,1,r) +3432*G(14,1,1,r) R(14,2,r) = +3/1105*G(0,3,3,r) -12/221*G(1,3,3,r) +24759/46189*G(2,3,3,r) -157752/46189*G(3,3,3,r) +48370/4199*G(4,3,3,r) +45192/1615*G(5,3,3,r) -3860577/7429*G(6,3,3,r) +832304/1311*G(7,3,3,r) +10592934/575*G(8,3,3,r) +7757064/115*G(9,3,3,r) +26880238/225*G(10,3,3,r) +360976/3*G(11,3,3,r) +2043756/29*G(12,3,3,r) +112112/5*G(13,3,3,r) +3003*G(14,3,3,r) R(14,4,r) = -35/46189*G(0,5,5,r) +1470/46189*G(1,5,5,r) -24108/46189*G(2,5,5,r) +19320/4199*G(3,5,5,r) -752175/52003*G(4,5,5,r) -1054590/7429*G(5,5,5,r) +11492152/10925*G(6,5,5,r) +6393744/575*G(7,5,5,r) +4867366/115*G(8,5,5,r) +1360436/15*G(9,5,5,r) +3506360/29*G(10,5,5,r) +103872912/1015*G(11,5,5,r) +8293857/155*G(12,5,5,r) +63063/4*G(13,5,5,r) +2002*G(14,5,5,r) R(14,6,r) = +7/12597*G(0,7,7,r) -168/4199*G(1,7,7,r) +647295/676039*G(2,7,7,r) -30580/3059*G(3,7,7,r) -31713/37145*G(4,7,7,r) +1812624/2185*G(5,7,7,r) +2050244/345*G(6,7,7,r) +500752/23*G(7,7,7,r) +1466806/29*G(8,7,7,r) +1890089168/23751*G(9,7,7,r) +541984839/6293*G(10,7,7,r) +3915483/62*G(11,7,7,r) +718055/24*G(12,7,7,r) +140140/17*G(13,7,7,r) +1001*G(14,7,7,r) R(14,8,r) = -45/52003*G(0,9,9,r) +4950/52003*G(1,9,9,r) -203346/68425*G(2,9,9,r) +942084/37145*G(3,9,9,r) +25909988/58995*G(4,9,9,r) +177112/69*G(5,9,9,r) +5978280/667*G(6,9,9,r) +4241557232/197925*G(7,9,9,r) +104138221/2821*G(8,9,9,r) +585717957/12586*G(9,9,9,r) +7934135/186*G(10,9,9,r) +470275/17*G(11,9,9,r) +1020162/85*G(12,9,9,r) +28028/9*G(13,9,9,r) +364*G(14,9,9,r) R(14,10,r) = +11/4025*G(0,11,11,r) -1716/4025*G(1,11,11,r) +2977/207*G(2,11,11,r) +166192/1035*G(3,11,11,r) +2768756/3335*G(4,11,11,r) +1803647504/650325*G(5,11,11,r) +1946628299/292175*G(6,11,11,r) +984897870/81809*G(7,11,11,r) +419037267/25172*G(8,11,11,r) +9281921/527*G(9,11,11,r) +4776189/340*G(10,11,11,r) +2085512/255*G(11,11,11,r) +363610/111*G(12,11,11,r) +15288/19*G(13,11,11,r) +91*G(14,11,11,r) R(14,12,r) = -13/675*G(0,13,13,r) +182/45*G(1,13,13,r) +49096/1305*G(2,13,13,r) +1638256/9135*G(3,13,13,r) +1552661/2697*G(4,13,13,r) +369980369/269700*G(5,13,13,r) +41018131/16182*G(6,13,13,r) +56577378/15283*G(7,13,13,r) +9048039/2108*G(8,13,13,r) +1200485/306*G(9,13,13,r) +183223612/66045*G(10,13,13,r) +3093064/2109*G(11,13,13,r) +31109/57*G(12,13,13,r) +637/5*G(13,13,13,r) +14*G(14,13,13,r) R(14,14,r) = +15/29*G(0,15,15,r) +1904/435*G(1,15,15,r) +88179/4495*G(2,15,15,r) +108927/1798*G(3,15,15,r) +3062059/21576*G(4,15,15,r) +4029025/15283*G(5,15,15,r) +24243219/61132*G(6,15,15,r) +256542/527*G(7,15,15,r) +1224405/2516*G(8,15,15,r) +4684680/11951*G(9,15,15,r) +175175/703*G(10,15,15,r) +11466/95*G(11,15,15,r) +17199/410*G(12,15,15,r) +28/3*G(13,15,15,r) +1*G(14,15,15,r) R(15,1,r) = -2/255*G(0,2,2,r) +8/85*G(1,2,2,r) -2844/4199*G(2,2,2,r) +45248/12597*G(3,2,2,r) -581700/46189*G(4,2,2,r) +87696/20995*G(5,2,2,r) +564872/1955*G(6,2,2,r) -11844096/7429*G(7,2,2,r) -809028/437*G(8,2,2,r) +935440/23*G(9,2,2,r) +94870776/575*G(10,2,2,r) +7303296/25*G(11,2,2,r) +74850776/261*G(12,2,2,r) +4708704/29*G(13,2,2,r) +1544400/31*G(14,2,2,r) +6435*G(15,2,2,r) R(15,3,r) = +4/4199*G(0,4,4,r) -120/4199*G(1,4,4,r) +17304/46189*G(2,4,4,r) -137760/46189*G(3,4,4,r) +1220040/96577*G(4,4,4,r) +150192/7429*G(5,4,4,r) -4318160/7429*G(6,4,4,r) +316800/437*G(7,4,4,r) +2945976/115*G(8,4,4,r) +7886032/69*G(9,4,4,r) +37173136/145*G(10,4,4,r) +9929920/29*G(11,4,4,r) +255471216/899*G(12,4,4,r) +71468397/496*G(13,4,4,r) +40950*G(14,4,4,r) +5005*G(15,4,4,r) R(15,5,r) = -18/46189*G(0,6,6,r) +1008/46189*G(1,6,6,r) -474120/1062347*G(2,6,6,r) +457920/96577*G(3,6,6,r) -141278/7429*G(4,6,6,r) -5833632/37145*G(5,6,6,r) +3103408/2185*G(6,6,6,r) +358656/23*G(7,6,6,r) +44129316/667*G(8,6,6,r) +4782624/29*G(9,6,6,r) +240429904/899*G(10,6,6,r) +2089523007/7192*G(11,6,6,r) +26031915/124*G(12,6,6,r) +1645280/17*G(13,6,6,r) +25740*G(14,6,6,r) +3003*G(15,6,6,r) R(15,7,r) = +8/22287*G(0,8,8,r) -240/7429*G(1,8,8,r) +48180/52003*G(2,8,8,r) -84656/7429*G(3,8,8,r) +47216/7429*G(4,8,8,r) +2367456/2185*G(5,8,8,r) +16216592/2001*G(6,8,8,r) +21417088/667*G(7,8,8,r) +373004016/4495*G(8,8,8,r) +135840196085/906192*G(9,8,8,r) +696495657/3596*G(10,8,8,r) +752747385/4216*G(11,8,8,r) +5844020/51*G(12,8,8,r) +97097/2*G(13,8,8,r) +450450/37*G(14,8,8,r) +1365*G(15,8,8,r) R(15,9,r) = -2/3059*G(0,10,10,r) +264/3059*G(1,10,10,r) -103012/32775*G(2,10,10,r) +620672/19665*G(3,10,10,r) +6925528/12673*G(4,10,10,r) +2236384/667*G(5,10,10,r) +3880232048/310155*G(6,10,10,r) +266140009509/8180900*G(7,10,10,r) +783317469/12586*G(8,10,10,r) +1367391410/15283*G(9,10,10,r) +51031695/527*G(10,10,10,r) +1322984/17*G(11,10,10,r) +24977524/555*G(12,10,10,r) +12418224/703*G(13,10,10,r) +4200*G(14,10,10,r) +455*G(15,10,10,r) R(15,11,r) = +4/1725*G(0,12,12,r) -728/1725*G(1,12,12,r) +163184/10005*G(2,12,12,r) +632128/3335*G(3,12,12,r) +64036688/62031*G(4,12,12,r) +30315784191/8270800*G(5,12,12,r) +425248747/44950*G(6,12,12,r) +3415288019/183396*G(7,12,12,r) +436422987/15283*G(8,12,12,r) +1166165/34*G(9,12,12,r) +100824152/3145*G(10,12,12,r) +80447432/3515*G(11,12,12,r) +8476104/703*G(12,12,12,r) +17647/4*G(13,12,12,r) +40950/41*G(14,12,12,r) +105*G(15,12,12,r) R(15,13,r) = -14/783*G(0,14,14,r) +1120/261*G(1,14,14,r) +37808/899*G(2,14,14,r) +13701337/64728*G(3,14,14,r) +8645/12*G(4,14,14,r) +27995968/15283*G(5,14,14,r) +501325825/137547*G(6,14,14,r) +354669315/61132*G(7,14,14,r) +290533815/38998*G(8,14,14,r) +828708400/107559*G(9,14,14,r) +13390520/2109*G(10,14,14,r) +5739825/1406*G(11,14,14,r) +243061/123*G(12,14,14,r) +27776/41*G(13,14,14,r) +6300/43*G(14,14,14,r) +15*G(15,14,14,r) R(15,15,r) = +16/31*G(0,16,16,r) +2295/496*G(1,16,16,r) +29925/1364*G(2,16,16,r) +302575/4216*G(3,16,16,r) +94185/527*G(4,16,16,r) +1496495/4216*G(5,16,16,r) +22447425/38998*G(6,16,16,r) +1141320375/1481924*G(7,16,16,r) +10179000/11951*G(8,16,16,r) +2177175/2812*G(9,16,16,r) +16459443/28823*G(10,16,16,r) +27405/82*G(11,16,16,r) +263900/1763*G(12,16,16,r) +45675/946*G(13,16,16,r) +10*G(14,16,16,r) +1*G(15,16,16,r) R(16,0,r) = +1/17*G(0,1,1,r) -6/17*G(1,1,1,r) +558/323*G(2,1,1,r) -140/19*G(3,1,1,r) +5670/221*G(4,1,1,r) -230076/4199*G(5,1,1,r) -629244/7429*G(6,1,1,r) +10211256/7429*G(7,1,1,r) -1923570/437*G(8,1,1,r) -265980/23*G(9,1,1,r) +9901892/115*G(10,1,1,r) +1897896/5*G(11,1,1,r) +57805748/87*G(12,1,1,r) +18378360/29*G(13,1,1,r) +10759320/31*G(14,1,1,r) +102960*G(15,1,1,r) +12870*G(16,1,1,r) R(16,2,r) = -3/1615*G(0,3,3,r) +12/323*G(1,3,3,r) -1563/4199*G(2,3,3,r) +10584/4199*G(3,3,3,r) -1053570/96577*G(4,3,3,r) +339768/37145*G(5,3,3,r) +1975743/7429*G(6,3,3,r) -700656/437*G(7,3,3,r) -389202/115*G(8,3,3,r) +1224808/23*G(9,3,3,r) +208101894/725*G(10,3,3,r) +19351024/29*G(11,3,3,r) +795937428/899*G(12,3,3,r) +22246224/31*G(13,3,3,r) +352755*G(14,3,3,r) +1647360/17*G(15,3,3,r) +11440*G(16,3,3,r) R(16,4,r) = +5/12597*G(0,5,5,r) -70/4199*G(1,5,5,r) +297612/1062347*G(2,5,5,r) -263480/96577*G(3,5,5,r) +105351/7429*G(4,5,5,r) +84546/7429*G(5,5,5,r) -39780664/58995*G(6,5,5,r) +349424/345*G(7,5,5,r) +23731638/667*G(8,5,5,r) +47351612/261*G(9,5,5,r) +1308410840/2697*G(10,5,5,r) +723664656/899*G(11,5,5,r) +27017809/31*G(12,5,5,r) +42013335/68*G(13,5,5,r) +4706130/17*G(14,5,5,r) +640640/9*G(15,5,5,r) +8008*G(16,5,5,r) R(16,6,r) = -21/96577*G(0,7,7,r) +1512/96577*G(1,7,7,r) -37719/96577*G(2,7,7,r) +36564/7429*G(3,7,7,r) -542311/22287*G(4,7,7,r) -378224/2185*G(5,7,7,r) +6425916/3335*G(6,7,7,r) +14425040/667*G(7,7,7,r) +89642058/899*G(8,7,7,r) +251172240/899*G(9,7,7,r) +473903001/899*G(10,7,7,r) +731092635/1054*G(11,7,7,r) +86899085/136*G(12,7,7,r) +6866860/17*G(13,7,7,r) +6171165/37*G(14,7,7,r) +768768/19*G(15,7,7,r) +4368*G(16,7,7,r) R(16,8,r) = +9/37145*G(0,9,9,r) -198/7429*G(1,9,9,r) +30602/33915*G(2,9,9,r) -287716/22287*G(3,9,9,r) +1817452/114057*G(4,9,9,r) +4678856/3335*G(5,9,9,r) +225257816/20677*G(6,9,9,r) +124334672/2697*G(7,9,9,r) +4032105/31*G(8,9,9,r) +56211365925/213962*G(9,9,9,r) +411732893/1054*G(10,9,9,r) +7307755/17*G(11,9,9,r) +217659442/629*G(12,9,9,r) +417196780/2109*G(13,9,9,r) +1441860/19*G(14,9,9,r) +17472*G(15,9,9,r) +1820*G(16,9,9,r) R(16,10,r) = -11/21735*G(0,11,11,r) +572/7245*G(1,11,11,r) -481/145*G(2,11,11,r) +696592/18009*G(3,11,11,r) +41766484/62031*G(4,11,11,r) +89318544/20677*G(5,11,11,r) +138307631/8091*G(6,11,11,r) +15339179218/320943*G(7,11,11,r) +42753013875/427924*G(8,11,11,r) +759269225/4743*G(9,11,11,r) +1494991927/7548*G(10,11,11,r) +132300168/703*G(11,11,11,r) +853297354/6327*G(12,11,11,r) +1338680/19*G(13,11,11,r) +1036035/41*G(14,11,11,r) +16640/3*G(15,11,11,r) +560*G(16,11,11,r) R(16,12,r) = +13/6525*G(0,13,13,r) -182/435*G(1,13,13,r) +82552/4495*G(2,13,13,r) +997424/4495*G(3,13,13,r) +404719/319*G(4,13,13,r) +7278147163/1528300*G(5,13,13,r) +1201706737/91698*G(6,13,13,r) +424892754/15283*G(7,13,13,r) +3632960331/77996*G(8,13,13,r) +4460887145/71706*G(9,13,13,r) +3953759524/59755*G(10,13,13,r) +38986584/703*G(11,13,13,r) +27939639/779*G(12,13,13,r) +707889/41*G(13,13,13,r) +250170/43*G(14,13,13,r) +13440/11*G(15,13,13,r) +120*G(16,13,13,r) R(16,14,r) = -15/899*G(0,15,15,r) +4080/899*G(1,15,15,r) +462213/9889*G(2,15,15,r) +83245365/336226*G(3,15,15,r) +108762745/122264*G(4,15,15,r) +36679825/15283*G(5,15,15,r) +11542465935/2261884*G(6,15,15,r) +3246539010/370481*G(7,15,15,r) +587512575/47804*G(8,15,15,r) +168597000/11951*G(9,15,15,r) +379954575/28823*G(10,15,15,r) +7710066/779*G(11,15,15,r) +20582289/3526*G(12,15,15,r) +1232980/473*G(13,15,15,r) +9115/11*G(14,15,15,r) +3840/23*G(15,15,15,r) +16*G(16,15,15,r) R(16,16,r) = +17/33*G(0,17,17,r) +912/187*G(1,17,17,r) +4560/187*G(2,17,17,r) +12880/153*G(3,17,17,r) +418600/1887*G(4,17,17,r) +5597280/11951*G(5,17,17,r) +9711520/11951*G(6,17,17,r) +14024400/11951*G(7,17,17,r) +694207800/489991*G(8,17,17,r) +41138240/28823*G(9,17,17,r) +39872448/33497*G(10,17,17,r) +15707328/19393*G(11,17,17,r) +1869920/4257*G(12,17,17,r) +138880/759*G(13,17,17,r) +59520/1081*G(14,17,17,r) +32/3*G(15,17,17,r) +1*G(16,17,17,r) R(17,1,r) = +2/323*G(0,2,2,r) -24/323*G(1,2,2,r) +1220/2261*G(2,2,2,r) -960/323*G(3,2,2,r) +1152900/96577*G(4,2,2,r) -2103024/96577*G(5,2,2,r) -4954488/37145*G(6,2,2,r) +9985536/7429*G(7,2,2,r) -4493060/1311*G(8,2,2,r) -9826960/483*G(9,2,2,r) +337263784/3335*G(10,2,2,r) +296103808/435*G(11,2,2,r) +1456935480/899*G(12,2,2,r) +1907025120/899*G(13,2,2,r) +51932400/31*G(14,2,2,r) +798720*G(15,2,2,r) +1487772/7*G(16,2,2,r) +24310*G(17,2,2,r) R(17,3,r) = -4/6783*G(0,4,4,r) +40/2261*G(1,4,4,r) -22744/96577*G(2,4,4,r) +192160/96577*G(3,4,4,r) -53592/5083*G(4,4,4,r) +602448/37145*G(5,4,4,r) +51338672/200583*G(6,4,4,r) -82729856/45885*G(7,4,4,r) -63181976/14007*G(8,4,4,r) +421968976/6003*G(9,4,4,r) +6192812912/13485*G(10,4,4,r) +3548184640/2697*G(11,4,4,r) +1992418064/899*G(12,4,4,r) +73688160/31*G(13,4,4,r) +11537760/7*G(14,4,4,r) +45208592/63*G(15,4,4,r) +6612320/37*G(16,4,4,r) +19448*G(17,4,4,r) R(17,5,r) = +18/96577*G(0,6,6,r) -1008/96577*G(1,6,6,r) +105624/482885*G(2,6,6,r) -19008/7429*G(3,6,6,r) +3205202/200583*G(4,6,6,r) +268576/334305*G(5,6,6,r) -50421168/63365*G(6,6,6,r) +45832448/30015*G(7,6,6,r) +3065298236/62031*G(8,6,6,r) +249043872/899*G(9,6,6,r) +2281563856/2697*G(10,6,6,r) +51472512/31*G(11,6,6,r) +68545386/31*G(12,6,6,r) +309704395/153*G(13,6,6,r) +139430720/111*G(14,6,6,r) +355026672/703*G(15,6,6,r) +356048/3*G(16,6,6,r) +12376*G(17,6,6,r) R(17,7,r) = -24/185725*G(0,8,8,r) +432/37145*G(1,8,8,r) -6116/17595*G(2,8,8,r) +1713712/334305*G(3,8,8,r) -19689488/646323*G(4,8,8,r) -179737376/950475*G(5,8,8,r) +808018064/310155*G(6,8,8,r) +3067985536/103385*G(7,8,8,r) +1972480048/13485*G(8,8,8,r) +404724320/899*G(9,8,8,r) +4307779476/4495*G(10,8,8,r) +4638637913/3162*G(11,8,8,r) +3079954696/1887*G(12,8,8,r) +920417498/703*G(13,8,8,r) +518191520/703*G(14,8,8,r) +1379728/5*G(15,8,8,r) +2524704/41*G(16,8,8,r) +6188*G(17,8,8,r) R(17,9,r) = +2/11799*G(0,10,10,r) -88/3933*G(1,10,10,r) +21892/24795*G(2,10,10,r) -4973696/342171*G(3,10,10,r) +33368552/1178589*G(4,10,10,r) +111638048/62031*G(5,10,10,r) +13449614192/930465*G(6,10,10,r) +873281024/13485*G(7,10,10,r) +530843170/2697*G(8,10,10,r) +240045432055/550188*G(9,10,10,r) +42567730205/58497*G(10,10,10,r) +33087600728/35853*G(11,10,10,r) +5610049588/6327*G(12,10,10,r) +446189170/703*G(13,10,10,r) +13428800/41*G(14,10,10,r) +14132560/123*G(15,10,10,r) +1051960/43*G(16,10,10,r) +2380*G(17,10,10,r) R(17,11,r) = -4/10005*G(0,12,12,r) +728/10005*G(1,12,12,r) -72240/20677*G(2,12,12,r) +967232/20677*G(3,12,12,r) +560846864/682341*G(4,12,12,r) +113664992/20677*G(5,12,12,r) +103109048/4495*G(6,12,12,r) +9404447195/137547*G(7,12,12,r) +87254342175/565471*G(8,12,12,r) +200838572935/740962*G(9,12,12,r) +13436610616/35853*G(10,12,12,r) +286708760/703*G(11,12,12,r) +9969315720/28823*G(12,12,12,r) +9180465/41*G(13,12,12,r) +188229600/1763*G(14,12,12,r) +16684080/473*G(15,12,12,r) +64736/9*G(16,12,12,r) +680*G(17,12,12,r) R(17,13,r) = +14/8091*G(0,14,14,r) -1120/2697*G(1,14,14,r) +203184/9889*G(2,14,14,r) +7648640/29667*G(3,14,14,r) +1387190/899*G(4,14,14,r) +36068669/5916*G(5,14,14,r) +30162536950/1696413*G(6,14,14,r) +14936516595/370481*G(7,14,14,r) +54073873425/740962*G(8,14,14,r) +3827304650/35853*G(9,14,14,r) +3646951880/28823*G(10,14,14,r) +183415050/1517*G(11,14,14,r) +162089018/1763*G(12,14,14,r) +1054690665/19393*G(13,14,14,r) +34220480/1419*G(14,14,14,r) +519824/69*G(15,14,14,r) +69360/47*G(16,14,14,r) +136*G(17,14,14,r) R(17,15,r) = -16/1023*G(0,16,16,r) +1632/341*G(1,16,16,r) +123348/2387*G(2,16,16,r) +1362490/4743*G(3,16,16,r) +63511280/58497*G(4,16,16,r) +3438401330/1111443*G(5,16,16,r) +2588371240/370481*G(6,16,16,r) +4756737180/370481*G(7,16,16,r) +9534782400/489991*G(8,16,16,r) +4931197700/201761*G(9,16,16,r) +31476128112/1239389*G(10,16,16,r) +10245816/473*G(11,16,16,r) +2608260928/174537*G(12,16,16,r) +265775720/32637*G(13,16,16,r) +10948640/3243*G(14,16,16,r) +141088/141*G(15,16,16,r) +9248/49*G(16,16,16,r) +17*G(17,16,16,r) R(17,17,r) = +18/35*G(0,18,18,r) +323/63*G(1,18,18,r) +2992/111*G(2,18,18,r) +68816/703*G(3,18,18,r) +1720400/6327*G(4,18,18,r) +426972/703*G(5,18,18,r) +32301360/28823*G(6,18,18,r) +349675040/201761*G(7,18,18,r) +19616769744/8675723*G(8,18,18,r) +3086554680/1239389*G(9,18,18,r) +182906944/79335*G(10,18,18,r) +216162752/121647*G(11,18,18,r) +52177216/46483*G(12,18,18,r) +5518744/9729*G(13,18,18,r) +508640/2303*G(14,18,18,r) +76296/1225*G(15,18,18,r) +34/3*G(16,18,18,r) +1*G(17,18,18,r) R(18,0,r) = -1/19*G(0,1,1,r) +6/19*G(1,1,1,r) -3510/2261*G(2,1,1,r) +2180/323*G(3,1,1,r) -185490/7429*G(4,1,1,r) +496188/7429*G(5,1,1,r) -1139292/37145*G(6,1,1,r) -298584/323*G(7,1,1,r) +2305446/437*G(8,1,1,r) -2897180/483*G(9,1,1,r) -246198524/3335*G(10,1,1,r) +25784616/145*G(11,1,1,r) +4152528380/2697*G(12,1,1,r) +3332969640/899*G(13,1,1,r) +147621240/31*G(14,1,1,r) +3659760*G(15,1,1,r) +11858418/7*G(16,1,1,r) +437580*G(17,1,1,r) +48620*G(18,1,1,r) R(18,2,r) = +3/2261*G(0,3,3,r) -60/2261*G(1,3,3,r) +105/391*G(2,3,3,r) -14040/7429*G(3,3,3,r) +898854/96577*G(4,3,3,r) -829224/37145*G(5,3,3,r) -754677/7429*G(6,3,3,r) +3836976/3059*G(7,3,3,r) -71388174/23345*G(8,3,3,r) -18288088/667*G(9,3,3,r) +520127322/4495*G(10,3,3,r) +981505360/899*G(11,3,3,r) +3000425220/899*G(12,3,3,r) +175563024/31*G(13,3,3,r) +41914665/7*G(14,3,3,r) +28375776/7*G(15,3,3,r) +63473410/37*G(16,3,3,r) +7876440/19*G(17,3,3,r) +43758*G(18,3,3,r) R(18,4,r) = -5/22287*G(0,5,5,r) +70/7429*G(1,5,5,r) -16884/104975*G(2,5,5,r) +801416/482885*G(3,5,5,r) -78573/7429*G(4,5,5,r) +178794/7429*G(5,5,5,r) +432144328/1710855*G(6,5,5,r) -107542864/50025*G(7,5,5,r) -568881222/103385*G(8,5,5,r) +767903444/8091*G(9,5,5,r) +1895963960/2697*G(10,5,5,r) +2118207312/899*G(11,5,5,r) +742259609/155*G(12,5,5,r) +6414954*G(13,5,5,r) +214946160/37*G(14,5,5,r) +22337194880/6327*G(15,5,5,r) +26253304/19*G(16,5,5,r) +1575288/5*G(17,5,5,r) +31824*G(18,5,5,r) R(18,6,r) = +231/2414425*G(0,7,7,r) -16632/2414425*G(1,7,7,r) +85041/482885*G(2,7,7,r) -5324/2185*G(3,7,7,r) +11613217/646323*G(4,7,7,r) -3852464/316825*G(5,7,7,r) -488512668/516925*G(6,7,7,r) +240964528/103385*G(7,7,7,r) +307751466/4495*G(8,7,7,r) +370348880/899*G(9,7,7,r) +6272105697/4495*G(10,7,7,r) +484648164/155*G(11,7,7,r) +181484303/37*G(12,7,7,r) +65599197664/11951*G(13,7,7,r) +3070849320/703*G(14,7,7,r) +229462464/95*G(15,7,7,r) +180757668/205*G(16,7,7,r) +190944*G(17,7,7,r) +18564*G(18,7,7,r) R(18,8,r) = -3/37145*G(0,9,9,r) +66/7429*G(1,9,9,r) -1012726/3231615*G(2,9,9,r) +3455452/646323*G(3,9,9,r) -132474524/3535767*G(4,9,9,r) -21087976/103385*G(5,9,9,r) +795369064/227447*G(6,9,9,r) +543367888/13485*G(7,9,9,r) +188791977/899*G(8,9,9,r) +628094610/899*G(9,9,9,r) +1883407526/1147*G(10,9,9,r) +33960893785/11951*G(11,9,9,r) +43946876974/11951*G(12,9,9,r) +7498395520/2109*G(13,9,9,r) +1971822720/779*G(14,9,9,r) +52742976/41*G(15,9,9,r) +18957380/43*G(16,9,9,r) +1002456/11*G(17,9,9,r) +8568*G(18,9,9,r) R(18,10,r) = +11/90045*G(0,11,11,r) -572/30015*G(1,11,11,r) +17927/20677*G(2,11,11,r) -9083984/558279*G(3,11,11,r) +29986028/682341*G(4,11,11,r) +520174704/227447*G(5,11,11,r) +766666663/40455*G(6,11,11,r) +240867560/2697*G(7,11,11,r) +9631914435/33263*G(8,11,11,r) +2316943278650/3334329*G(9,11,11,r) +91513465043/71706*G(10,11,11,r) +21744445008/11951*G(11,11,11,r) +523145697620/259407*G(12,11,11,r) +1341948160/779*G(13,11,11,r) +1959852960/1763*G(14,11,11,r) +742630720/1419*G(15,11,11,r) +1861636/11*G(16,11,11,r) +771120/23*G(17,11,11,r) +3060*G(18,11,11,r) R(18,12,r) = -13/40455*G(0,13,13,r) +182/2697*G(1,13,13,r) -36312/9889*G(2,13,13,r) +552976/9889*G(3,13,13,r) +9836965/9889*G(4,13,13,r) +31097794/4495*G(5,13,13,r) +3024066220/99789*G(6,13,13,r) +1027786250790/10743949*G(7,13,13,r) +342263486565/1481924*G(8,13,13,r) +15750774325/35853*G(9,13,13,r) +327120072136/489991*G(10,13,13,r) +23448005880/28823*G(11,13,13,r) +26506963665/33497*G(12,13,13,r) +11765913432/19393*G(13,13,13,r) +169559760/473*G(14,13,13,r) +39801216/253*G(15,13,13,r) +52103640/1081*G(16,13,13,r) +9180*G(17,13,13,r) +816*G(18,13,13,r) R(18,14,r) = +15/9889*G(0,15,15,r) -4080/9889*G(1,15,15,r) +7909947/346115*G(2,15,15,r) +267444/899*G(3,15,15,r) +1994905/1073*G(4,15,15,r) +82783527400/10743949*G(5,15,15,r) +8213120370/346579*G(6,15,15,r) +21139520064/370481*G(7,15,15,r) +54205674120/489991*G(8,15,15,r) +600915744000/3429937*G(9,15,15,r) +282438842400/1239389*G(10,15,15,r) +89582281776/368467*G(11,15,15,r) +20469728916/96965*G(12,15,15,r) +1599313184/10879*G(13,15,15,r) +86661080/1081*G(14,15,15,r) +35634720/1081*G(15,15,15,r) +470458/49*G(16,15,15,r) +44064/25*G(17,15,15,r) +153*G(18,15,15,r) R(18,16,r) = -17/1155*G(0,17,17,r) +1938/385*G(1,17,17,r) +23142/407*G(2,17,17,r) +2093552/6327*G(3,17,17,r) +35958200/27417*G(4,17,17,r) +2763864/703*G(5,17,17,r) +270465832/28823*G(6,17,17,r) +3699636720/201761*G(7,17,17,r) +258384143160/8675723*G(8,17,17,r) +1223862640/30229*G(9,17,17,r) +7722438768/167485*G(10,17,17,r) +97692848448/2230195*G(11,17,17,r) +158237492192/4601817*G(12,17,17,r) +783071408/35673*G(13,17,17,r) +589017360/52969*G(14,17,17,r) +15813536/3675*G(15,17,17,r) +29869/25*G(16,17,17,r) +2754/13*G(17,17,17,r) +18*G(18,17,17,r) R(18,18,r) = +19/37*G(0,19,19,r) +3780/703*G(1,19,19,r) +270963/9139*G(2,19,19,r) +1032240/9139*G(3,19,19,r) +9501300/28823*G(4,19,19,r) +22362480/28823*G(5,19,19,r) +1877516550/1239389*G(6,19,19,r) +3089855808/1239389*G(7,19,19,r) +4321176552/1239389*G(8,19,19,r) +3200871520/770431*G(9,19,19,r) +8025042168/1905803*G(10,19,19,r) +167712480/46483*G(11,19,19,r) +2795208/1081*G(12,19,19,r) +8239968/5405*G(13,19,19,r) +5049/7*G(14,19,19,r) +17136/65*G(15,19,19,r) +48195/689*G(16,19,19,r) +12*G(17,19,19,r) +1*G(18,19,19,r) R(19,1,r) = -2/399*G(0,2,2,r) +8/133*G(1,2,2,r) -22860/52003*G(2,2,2,r) +55360/22287*G(3,2,2,r) -402036/37145*G(4,2,2,r) +1078704/37145*G(5,2,2,r) +3979976/111435*G(6,2,2,r) -47810048/52003*G(7,2,2,r) +405266004/88711*G(8,2,2,r) -110370832/210105*G(9,2,2,r) -31241755688/310155*G(10,2,2,r) +616497024/4495*G(11,2,2,r) +19996032680/8091*G(12,2,2,r) +7193615520/899*G(13,2,2,r) +2945597616/217*G(14,2,2,r) +98668544/7*G(15,2,2,r) +2410686564/259*G(16,2,2,r) +141775920/37*G(17,2,2,r) +2700280/3*G(18,2,2,r) +92378*G(19,2,2,r) R(19,3,r) = +20/52003*G(0,4,4,r) -600/52003*G(1,4,4,r) +28824/185725*G(2,4,4,r) -2976/2185*G(3,4,4,r) +206712/25415*G(4,4,4,r) -11088/437*G(5,4,4,r) -47967920/646323*G(6,4,4,r) +2822312064/2217775*G(7,4,4,r) -2449063656/723695*G(8,4,4,r) -10680866768/310155*G(9,4,4,r) +125284016/899*G(10,4,4,r) +1487137600/899*G(11,4,4,r) +27573474864/4495*G(12,4,4,r) +398020896/31*G(13,4,4,r) +4455423648/259*G(14,4,4,r) +3976727040/259*G(15,4,4,r) +337609800/37*G(16,4,4,r) +34775829/10*G(17,4,4,r) +31593276/41*G(18,4,4,r) +75582*G(19,4,4,r) R(19,5,r) = -18/185725*G(0,6,6,r) +1008/185725*G(1,6,6,r) -11160/96577*G(2,6,6,r) +690624/482885*G(3,6,6,r) -34846042/3231615*G(4,6,6,r) +176183392/5386025*G(5,6,6,r) +2465763664/9821575*G(6,6,6,r) -1880320/713*G(7,6,6,r) -661958388/103385*G(8,6,6,r) +585474912/4495*G(9,6,6,r) +33009875184/31465*G(10,6,6,r) +17807257728/4495*G(11,6,6,r) +10706851350/1147*G(12,6,6,r) +552656832/37*G(13,6,6,r) +619038816/37*G(14,6,6,r) +46262353368/3515*G(15,6,6,r) +1462518024/205*G(16,6,6,r) +728769600/287*G(17,6,6,r) +22976928/43*G(18,6,6,r) +50388*G(19,6,6,r) R(19,7,r) = +88/1671525*G(0,8,8,r) -176/37145*G(1,8,8,r) +484/3335*G(2,8,8,r) -7575568/3231615*G(3,8,8,r) +134393168/6678671*G(4,8,8,r) -276048864/9821575*G(5,8,8,r) -3830776432/3411705*G(6,8,8,r) +363450752/103385*G(7,8,8,r) +2121903792/22475*G(8,8,8,r) +4857822112/8091*G(9,8,8,r) +367685602284/166315*G(10,8,8,r) +6324894576/1147*G(11,8,8,r) +1095910816/111*G(12,8,8,r) +9125140948/703*G(13,8,8,r) +362429741520/28823*G(14,8,8,r) +1818707736/205*G(15,8,8,r) +7811073504/1763*G(16,8,8,r) +701245818/473*G(17,8,8,r) +4467736/15*G(18,8,8,r) +27132*G(19,8,8,r) R(19,9,r) = -2/38019*G(0,10,10,r) +88/12673*G(1,10,10,r) -1682044/5892945*G(2,10,10,r) +19720064/3535767*G(3,10,10,r) -196202440/4321493*G(4,10,10,r) -49241248/227447*G(5,10,10,r) +7213397296/1550775*G(6,10,10,r) +1217106432/22475*G(7,10,10,r) +9849771594/33263*G(8,10,10,r) +35014523544/33263*G(9,10,10,r) +3084141060/1147*G(10,10,10,r) +61583718833/11951*G(11,10,10,r) +652681716544/86469*G(12,10,10,r) +244594116480/28823*G(13,10,10,r) +12818478720/1763*G(14,10,10,r) +90380699240/19393*G(15,10,10,r) +5110632072/2365*G(16,10,10,r) +78585696/115*G(17,10,10,r) +6186096/47*G(18,10,10,r) +11628*G(19,10,10,r) R(19,11,r) = +28/310155*G(0,12,12,r) -5096/310155*G(1,12,12,r) +582512/682341*G(2,12,12,r) -4120256/227447*G(3,12,12,r) +302446864/4776387*G(4,12,12,r) +297707808/103385*G(5,12,12,r) +4086939976/166315*G(6,12,12,r) +12096360640/99789*G(7,12,12,r) +13843245780/33263*G(8,12,12,r) +6343437415315/5927696*G(9,12,12,r) +1046029129574/489991*G(10,12,12,r) +677820289757/201761*G(11,12,12,r) +5196232279680/1239389*G(12,12,12,r) +80179838410/19393*G(13,12,12,r) +61735027536/19393*G(14,12,12,r) +20366869992/10879*G(15,12,12,r) +876622544/1081*G(16,12,12,r) +22875795/94*G(17,12,12,r) +2209320/49*G(18,12,12,r) +3876*G(19,12,12,r) R(19,13,r) = -70/267003*G(0,14,14,r) +5600/89001*G(1,14,14,r) -45968/11935*G(2,14,14,r) +41219968/623007*G(3,14,14,r) +119167582/99789*G(4,14,14,r) +286706960/33263*G(5,14,14,r) +11822069000/299367*G(6,14,14,r) +1410995192334/10743949*G(7,14,14,r) +5115767206680/15189721*G(8,14,14,r) +21211615518080/30869433*G(9,14,14,r) +29497999273600/26027169*G(10,14,14,r) +1091330038500/717541*G(11,14,14,r) +482677390312/290895*G(12,14,14,r) +651576771776/446039*G(13,14,14,r) +522995986464/511313*G(14,14,14,r) +601279120/1081*G(15,14,14,r) +520980300/2303*G(16,14,14,r) +79187904/1225*G(17,14,14,r) +11552*G(18,14,14,r) +969*G(19,14,14,r) R(19,15,r) = +16/11935*G(0,16,16,r) -4896/11935*G(1,16,16,r) +2233260/88319*G(2,16,16,r) +391248/1147*G(3,16,16,r) +33120552/14911*G(4,16,16,r) +5670167/589*G(5,16,16,r) +27788077716/893513*G(6,16,16,r) +494724338550/6254591*G(7,16,16,r) +1415216499840/8675723*G(8,16,16,r) +2404849903170/8675723*G(9,16,16,r) +2423334317976/6196945*G(10,16,16,r) +1022788009044/2230195*G(11,16,16,r) +9334839756320/20963833*G(12,16,16,r) +181289560872/511313*G(13,16,16,r) +524760896/2303*G(14,16,16,r) +6638708624/57575*G(15,16,16,r) +54164448/1225*G(16,16,16,r) +313695/26*G(17,16,16,r) +110466/53*G(18,16,16,r) +171*G(19,16,16,r) R(19,17,r) = -18/1295*G(0,18,18,r) +1368/259*G(1,18,18,r) +29964/481*G(2,18,18,r) +17302923/45695*G(3,18,18,r) +45246520/28823*G(4,18,18,r) +142223904/28823*G(5,18,18,r) +15363023760/1239389*G(6,18,18,r) +2445134505840/95432953*G(7,18,18,r) +1921632824592/43378615*G(8,18,18,r) +1842055833024/28505947*G(9,18,18,r) +760069805792/9529015*G(10,18,18,r) +158514848076/1905803*G(11,18,18,r) +23697773424/325381*G(12,18,18,r) +1431719872/27025*G(13,18,18,r) +362504736/11515*G(14,18,18,r) +237323196/15925*G(15,18,18,r) +3725754/689*G(16,18,18,r) +74856/53*G(17,18,18,r) +12996/55*G(18,18,18,r) +19*G(19,18,18,r) R(19,19,r) = +20/39*G(0,20,20,r) +1463/260*G(1,20,20,r) +86526/2665*G(2,20,20,r) +37145/287*G(3,20,20,r) +697680/1763*G(4,20,20,r) +18968175/19393*G(5,20,20,r) +195133344/96965*G(6,20,20,r) +710842896/202745*G(7,20,20,r) +9951800544/1905803*G(8,20,20,r) +38173250797/5717409*G(9,20,20,r) +684485876360/93384347*G(10,20,20,r) +56003389884/8134525*G(11,20,20,r) +1039067744/189175*G(12,20,20,r) +22479831/6110*G(13,20,20,r) +49046904/24115*G(14,20,20,r) +1869980/2067*G(15,20,20,r) +908276/2915*G(16,20,20,r) +120213/1540*G(17,20,20,r) +38/3*G(18,20,20,r) +1*G(19,20,20,r) R(20,0,r) = +1/21*G(0,1,1,r) -2/7*G(1,1,1,r) +4310/3059*G(2,1,1,r) -8140/1311*G(3,1,1,r) +9354/391*G(4,1,1,r) -2696628/37145*G(5,1,1,r) +12033164/111435*G(6,1,1,r) +26287976/52003*G(7,1,1,r) -416569582/88711*G(8,1,1,r) +624372892/42021*G(9,1,1,r) +1241175364/62031*G(10,1,1,r) -4149691832/13485*G(11,1,1,r) +5152940/261*G(12,1,1,r) +4840616040/899*G(13,1,1,r) +3963016200/217*G(14,1,1,r) +215345936/7*G(15,1,1,r) +8104579626/259*G(16,1,1,r) +745490460/37*G(17,1,1,r) +24231460/3*G(18,1,1,r) +1847560*G(19,1,1,r) +184756*G(20,1,1,r) R(20,2,r) = -3/3059*G(0,3,3,r) +60/3059*G(1,3,3,r) -1485/7429*G(2,3,3,r) +10728/7429*G(3,3,3,r) -171446/22287*G(4,3,3,r) +948376/37145*G(5,3,3,r) +2609607/215441*G(6,3,3,r) -617812624/798399*G(7,3,3,r) +3018444286/723695*G(8,3,3,r) +44219032/20677*G(9,3,3,r) -1660538594/13485*G(10,3,3,r) +75300560/899*G(11,3,3,r) +22993942140/6293*G(12,3,3,r) +468268944/31*G(13,3,3,r) +8378752005/259*G(14,3,3,r) +11169636192/259*G(15,3,3,r) +4199475830/111*G(16,3,3,r) +21968760*G(17,3,3,r) +334500738/41*G(18,3,3,r) +36951200/21*G(19,3,3,r) +167960*G(20,3,3,r) R(20,4,r) = +1/7429*G(0,5,5,r) -42/7429*G(1,5,5,r) +18116/185725*G(2,5,5,r) -38808/37145*G(3,5,5,r) +1603503/215441*G(4,5,5,r) -6244238/215441*G(5,5,5,r) -288296008/5892945*G(6,5,5,r) +699874032/516925*G(7,5,5,r) -4770222002/1137235*G(8,5,5,r) -115293892/2697*G(9,5,5,r) +1126535960/6293*G(10,5,5,r) +15368658864/6293*G(11,5,5,r) +60061649973/5735*G(12,5,5,r) +958687938/37*G(13,5,5,r) +1557157360/37*G(14,5,5,r) +1738142560/37*G(15,5,5,r) +1493430246/41*G(16,5,5,r) +27742221936/1435*G(17,5,5,r) +2019954144/301*G(18,5,5,r) +15116400/11*G(19,5,5,r) +125970*G(20,5,5,r) R(20,6,r) = -77/1671525*G(0,7,7,r) +616/185725*G(1,7,7,r) -92807/1077205*G(2,7,7,r) +4070924/3231615*G(3,7,7,r) -74004931/6678671*G(4,7,7,r) +415310896/9821575*G(5,7,7,r) +4230589636/17058525*G(6,7,7,r) -3724909552/1137235*G(7,7,7,r) -225099178/31465*G(8,7,7,r) +10211579440/56637*G(9,7,7,r) +1791363050763/1164205*G(10,7,7,r) +36572615508/5735*G(11,7,7,r) +1877161429/111*G(12,7,7,r) +1155749408/37*G(13,7,7,r) +63029030680/1517*G(14,7,7,r) +1095142982208/27265*G(15,7,7,r) +1727920621908/61705*G(16,7,7,r) +45430223904/3311*G(17,7,7,r) +147922372/33*G(18,7,7,r) +20155200/23*G(19,7,7,r) +77520*G(20,7,7,r) R(20,8,r) = +33/1077205*G(0,9,9,r) -726/215441*G(1,9,9,r) +4067778/33393355*G(2,9,9,r) -15171156/6678671*G(3,9,9,r) +113796956/5073057*G(4,9,9,r) -162453928/3411705*G(5,9,9,r) -302523096/227447*G(6,9,9,r) +2262448/435*G(7,9,9,r) +4303217669/33263*G(8,9,9,r) +28627818570/33263*G(9,9,9,r) +11687533858/3441*G(10,9,9,r) +342562220/37*G(11,9,9,r) +28042902888/1517*G(12,9,9,r) +7193433660160/259407*G(13,9,9,r) +1055136546560/33497*G(14,9,9,r) +523038005568/19393*G(15,9,9,r) +8098054380/473*G(16,9,9,r) +1974504168/253*G(17,9,9,r) +2607765048/1081*G(18,9,9,r) +452200*G(19,9,9,r) +38760*G(20,9,9,r) R(20,10,r) = -11/310155*G(0,11,11,r) +572/103385*G(1,11,11,r) -536627/2047023*G(2,11,11,r) +11905712/2047023*G(3,11,11,r) -86495524/1592129*G(4,11,11,r) -69866192/310155*G(5,11,11,r) +1019011059/166315*G(6,11,11,r) +2396879640/33263*G(7,11,11,r) +13674069435/33263*G(8,11,11,r) +1775717580/1147*G(9,11,11,r) +6444200763/1517*G(10,11,11,r) +91348730927168/10289811*G(11,11,11,r) +53648886608720/3718167*G(12,11,11,r) +6771488916480/368467*G(13,11,11,r) +354978544960/19393*G(14,11,11,r) +153428298816/10879*G(15,11,11,r) +8897306796/1081*G(16,11,11,r) +3796309440/1081*G(17,11,11,r) +50543040/49*G(18,11,11,r) +186048*G(19,11,11,r) +15504*G(20,11,11,r) R(20,12,r) = +91/1335015*G(0,13,13,r) -1274/89001*G(1,13,13,r) +524824/623007*G(2,13,13,r) -12501392/623007*G(3,13,13,r) +95448115/1097679*G(4,13,13,r) +57842194/16095*G(5,13,13,r) +122745932180/3891771*G(6,13,13,r) +5396443080/33263*G(7,13,13,r) +27576771495/47027*G(8,13,13,r) +49483207213700/30869433*G(9,13,13,r) +1520762746099168/442461873*G(10,13,13,r) +240863826505120/40899837*G(11,13,13,r) +8983938781220/1105401*G(12,13,13,r) +4029812295496/446039*G(13,13,13,r) +4108509490960/511313*G(14,13,13,r) +2914540384/517*G(15,13,13,r) +161442428310/52969*G(16,13,13,r) +59942340/49*G(17,13,13,r) +342608*G(18,13,13,r) +775200/13*G(19,13,13,r) +4845*G(20,13,13,r) R(20,14,r) = -15/69223*G(0,15,15,r) +4080/69223*G(1,15,15,r) -1665711/413105*G(2,15,15,r) +28383948/365893*G(3,15,15,r) +1845925145/1297257*G(4,15,15,r) +4600998200/432419*G(5,15,15,r) +69328247490/1363783*G(6,15,15,r) +1109269233024/6254591*G(7,15,15,r) +4167481088160/8675723*G(8,15,15,r) +9052153344000/8675723*G(9,15,15,r) +2292580804800/1239389*G(10,15,15,r) +22876007635728/8474741*G(11,15,15,r) +340490920890276/104819165*G(12,15,15,r) +4926495868064/1533939*G(13,15,15,r) +1505974994120/582659*G(14,15,15,r) +88271986464/52969*G(15,15,15,r) +41153226/49*G(16,15,15,r) +103480992/325*G(17,15,15,r) +58753377/689*G(18,15,15,r) +129200/9*G(19,15,15,r) +1140*G(20,15,15,r) R(20,16,r) = +17/14245*G(0,17,17,r) -5814/14245*G(1,17,17,r) +147326/5291*G(2,17,17,r) +187036/481*G(3,17,17,r) +51932850/19721*G(4,17,17,r) +2401933608/201761*G(5,17,17,r) +49900249656/1239389*G(6,17,17,r) +10277729973360/95432953*G(7,17,17,r) +2038248795960/8675723*G(8,17,17,r) +12123726360720/28505947*G(9,17,17,r) +116740978353648/181051285*G(10,17,17,r) +86098733545136/104819165*G(11,17,17,r) +21996977542072/25054337*G(12,17,17,r) +65154072432/83237*G(13,17,17,r) +30502043280/52969*G(14,17,17,r) +5473847136/15925*G(15,17,17,r) +2795762421/17225*G(16,17,17,r) +40185722/689*G(17,17,17,r) +494114/33*G(18,17,17,r) +17100/7*G(19,17,17,r) +190*G(20,17,17,r) R(20,18,r) = -19/1443*G(0,19,19,r) +2660/481*G(1,19,19,r) +1340647/19721*G(2,19,19,r) +4574240/10619*G(3,19,19,r) +850894200/456617*G(4,19,19,r) +4394759760/717541*G(5,19,19,r) +11579164950/717541*G(6,19,19,r) +52703608896/1500313*G(7,19,19,r) +4534223650488/70514711*G(8,19,19,r) +571501060480/5717409*G(9,19,19,r) +12378776156032/93384347*G(10,19,19,r) +341667591200/2277667*G(11,19,19,r) +1092378248/7567*G(12,19,19,r) +57688554528/491855*G(13,19,19,r) +383500161/4823*G(14,19,19,r) +456866704/10335*G(15,19,19,r) +11451965/583*G(16,19,19,r) +516724/77*G(17,19,19,r) +34751/21*G(18,19,19,r) +7600/29*G(19,19,19,r) +20*G(20,19,19,r) R(20,20,r) = +21/41*G(0,21,21,r) +5060/861*G(1,21,21,r) +437000/12341*G(2,21,21,r) +20007000/135751*G(3,21,21,r) +9132825/19393*G(4,21,21,r) +543585744/446039*G(5,21,21,r) +5017714560/1905803*G(6,21,21,r) +27643890400/5717409*G(7,21,21,r) +712323818700/93384347*G(8,21,21,r) +970725424656/93384347*G(9,21,21,r) +418744300832/34165005*G(10,21,21,r) +94460704/7567*G(11,21,21,r) +4383567045/401051*G(12,21,21,r) +9082760/1113*G(13,21,21,r) +2991968/583*G(14,21,21,r) +10899312/4081*G(15,21,21,r) +776815/693*G(16,21,21,r) +74100/203*G(17,21,21,r) +148200/1711*G(18,21,21,r) +40/3*G(19,21,21,r) +1*G(20,21,21,r) R(21,1,r) = +2/483*G(0,2,2,r) -8/161*G(1,2,2,r) +1116/3059*G(2,2,2,r) -2752/1311*G(3,2,2,r) +71700/7429*G(4,2,2,r) -1161072/37145*G(5,2,2,r) +3755752/170085*G(6,2,2,r) +833710592/1508087*G(7,2,2,r) -11245378716/2750041*G(8,2,2,r) +13847856880/1302651*G(9,2,2,r) +2586794600/62031*G(10,2,2,r) -1617822336/4495*G(11,2,2,r) -3238560520/8091*G(12,2,2,r) +6887244000/899*G(13,2,2,r) +284952891600/8029*G(14,2,2,r) +19998937088/259*G(15,2,2,r) +26407075596/259*G(16,2,2,r) +3246305040/37*G(17,2,2,r) +6121534760/123*G(18,2,2,r) +739024000/41*G(19,2,2,r) +162954792/43*G(20,2,2,r) +352716*G(21,2,2,r) R(21,3,r) = -4/15295*G(0,4,4,r) +24/3059*G(1,4,4,r) -11848/111435*G(2,4,4,r) +928/969*G(3,4,4,r) -1326600/215441*G(4,4,4,r) +27051024/1077205*G(5,4,4,r) -144144/13547*G(6,4,4,r) -9532009344/13750205*G(7,4,4,r) +6871032792/1592129*G(8,4,4,r) +174556304/62031*G(9,4,4,r) -670255664/4495*G(10,4,4,r) +103837760/2697*G(11,4,4,r) +173751547216/33263*G(12,4,4,r) +29942246880/1147*G(13,4,4,r) +17521486560/259*G(14,4,4,r) +28743593472/259*G(15,4,4,r) +186544864440/1517*G(16,4,4,r) +3844914480/41*G(17,4,4,r) +85863503440/1763*G(18,4,4,r) +7803085680/473*G(19,4,4,r) +3292016*G(20,4,4,r) +293930*G(21,4,4,r) R(21,5,r) = +2/37145*G(0,6,6,r) -112/37145*G(1,6,6,r) +69912/1077205*G(2,6,6,r) -10560/12673*G(3,6,6,r) +139809670/20036013*G(4,6,6,r) -1097448352/33393355*G(5,6,6,r) -493859184/21607465*G(6,6,6,r) +54176512/36685*G(7,6,6,r) -113050476/20677*G(8,6,6,r) -47605856/899*G(9,6,6,r) +56218027216/232841*G(10,6,6,r) +3819284352/1073*G(11,6,6,r) +19541165202/1147*G(12,6,6,r) +1781586240/37*G(13,6,6,r) +138757919520/1517*G(14,6,6,r) +185962613760/1517*G(15,6,6,r) +207770983860/1763*G(16,6,6,r) +10995729674436/135751*G(17,6,6,r) +18400689840/473*G(18,6,6,r) +285448020/23*G(19,6,6,r) +111105540/47*G(20,6,6,r) +203490*G(21,6,6,r) R(21,7,r) = -1144/48474225*G(0,8,8,r) +2288/1077205*G(1,8,8,r) -2207524/33393355*G(2,8,8,r) +112928816/100180065*G(3,8,8,r) -839967856/73465381*G(4,8,8,r) +5717126688/108037325*G(5,8,8,r) +821206064/3411705*G(6,8,8,r) -422134144/103385*G(7,8,8,r) -1268555184/166315*G(8,8,8,r) +74917254880/299367*G(9,8,8,r) +370253390052/166315*G(10,8,8,r) +11404240848/1147*G(11,8,8,r) +132141577568/4551*G(12,8,8,r) +91514975552/1517*G(13,8,8,r) +6026005196640/65231*G(14,8,8,r) +10243007156784/96965*G(15,8,8,r) +1747106348832/19393*G(16,8,8,r) +614655952092/10879*G(17,8,8,r) +82009762016/3243*G(18,8,8,r) +359092020/47*G(19,8,8,r) +1395360*G(20,8,8,r) +116280*G(21,8,8,r) R(21,9,r) = +22/1178589*G(0,10,10,r) -968/392863*G(1,10,10,r) +2242604/21607465*G(2,10,10,r) -9563008/4321493*G(3,10,10,r) +107556008/4321493*G(4,10,10,r) -1473696/20677*G(5,10,10,r) -5996965968/3825245*G(6,10,10,r) +250753536/33263*G(7,10,10,r) +5853531150/33263*G(8,10,10,r) +40452189960/33263*G(9,10,10,r) +239420383020/47027*G(10,10,10,r) +22696337664/1517*G(11,10,10,r) +52091040144/1591*G(12,10,10,r) +747522938987160/13633279*G(13,10,10,r) +1377757166400/19393*G(14,10,10,r) +31769492754480/446039*G(15,10,10,r) +2544547542264/46483*G(16,10,10,r) +34185872322/1081*G(17,10,10,r) +623764680/47*G(18,10,10,r) +3813984*G(19,10,10,r) +670320*G(20,10,10,r) +54264*G(21,10,10,r) R(21,11,r) = -28/1137235*G(0,12,12,r) +5096/1137235*G(1,12,12,r) -165424/682341*G(2,12,12,r) +1378496/227447*G(3,12,12,r) -1033088368/16066029*G(4,12,12,r) -874704672/3825245*G(5,12,12,r) +3455547480/432419*G(6,12,12,r) +9476622400/99789*G(7,12,12,r) +767639941740/1363783*G(8,12,12,r) +104916422520/47027*G(9,12,12,r) +425143975776/65231*G(10,12,12,r) +1400999520064768/95432953*G(11,12,12,r) +355542209561760/13633279*G(12,12,12,r) +16462001354960/446039*G(13,12,12,r) +873553143546720/20963833*G(14,12,12,r) +1734488407008/46483*G(15,12,12,r) +28269029768/1081*G(16,12,12,r) +658982016/47*G(17,12,12,r) +271668384/49*G(18,12,12,r) +19772160/13*G(19,12,12,r) +13674528/53*G(20,12,12,r) +20349*G(21,12,12,r) R(21,13,r) = +14/267003*G(0,14,14,r) -1120/89001*G(1,14,14,r) +2132752/2561251*G(2,14,14,r) -509978240/23051259*G(3,14,14,r) +149692450/1297257*G(4,14,14,r) +1923212528/432419*G(5,14,14,r) +16971428600/423243*G(6,14,14,r) +292422883200/1363783*G(7,14,14,r) +1642418761050/2022161*G(8,14,14,r) +2014658467554200/858896577*G(9,14,14,r) +139547818614880/26027169*G(10,14,14,r) +3103300519269600/313565417*G(11,14,14,r) +936984868998776/62891499*G(12,14,14,r) +384487434364600/20963833*G(13,14,14,r) +9410584814880/511313*G(14,14,14,r) +80651454944/5405*G(15,14,14,r) +22162026132/2303*G(16,14,14,r) +15343876512/3185*G(17,14,14,r) +1241782240/689*G(18,14,14,r) +25087410/53*G(19,14,14,r) +854658/11*G(20,14,14,r) +5985*G(21,14,14,r) R(21,15,r) = -16/88319*G(0,16,16,r) +4896/88319*G(1,16,16,r) -439812/104377*G(2,16,16,r) +1345200/14911*G(3,16,16,r) +1029355800/611351*G(4,16,16,r) +612471600/47027*G(5,16,16,r) +130883823000/2022161*G(6,16,16,r) +698370068408940/2958421543*G(7,16,16,r) +64146270254400/95432953*G(8,16,16,r) +308296433207100/199541629*G(9,16,16,r) +3914147304117648/1339779509*G(10,16,16,r) +4183890731568/911471*G(11,16,16,r) +126120725543072/20963833*G(12,16,16,r) +7102158000/1081*G(13,16,16,r) +314866729440/52969*G(14,16,16,r) +659944261152/149695*G(15,16,16,r) +444876396192/168805*G(16,16,16,r) +853067643/689*G(17,16,16,r) +769088840/1749*G(18,16,16,r) +1219230/11*G(19,16,16,r) +17640*G(20,16,16,r) +1330*G(21,16,16,r) R(21,17,r) = +18/16835*G(0,18,18,r) -1368/3367*G(1,18,18,r) +602052/19721*G(2,18,18,r) +8695104/19721*G(3,18,18,r) +202222900/65231*G(4,18,18,r) +10466230914/717541*G(5,18,18,r) +36950271120/717541*G(6,18,18,r) +16675031881440/115524101*G(7,18,18,r) +3805890277968/11479139*G(8,18,18,r) +44826173915580/70514711*G(9,18,18,r) +425952859792/414305*G(10,18,18,r) +2686038356352/1905803*G(11,18,18,r) +533157645072/325381*G(12,18,18,r) +2407285408/1495*G(13,18,18,r) +2107055088864/1586767*G(14,18,18,r) +766579675224/844025*G(15,18,18,r) +3837179922/7579*G(16,18,18,r) +2465706/11*G(17,18,18,r) +833796/11*G(18,18,18,r) +532880/29*G(19,18,18,r) +167580/59*G(20,18,18,r) +210*G(21,18,18,r) R(21,19,r) = -20/1599*G(0,20,20,r) +3080/533*G(1,20,20,r) +1694088/22919*G(2,20,20,r) +66161800/135751*G(3,20,20,r) +42579000/19393*G(4,20,20,r) +3357366975/446039*G(5,20,20,r) +434757090432/20963833*G(6,20,20,r) +90277047792/1905803*G(7,20,20,r) +174156509520/1905803*G(8,20,20,r) +860633290696/5717409*G(9,20,20,r) +19885961866784/93384347*G(10,20,20,r) +421672582656/1626905*G(11,20,20,r) +543432430112/2005255*G(12,20,20,r) +7845461019/32383*G(13,20,20,r) +9743984928/53053*G(14,20,20,r) +2651631640/22737*G(15,20,20,r) +35518372/583*G(16,20,20,r) +56968308/2233*G(17,20,20,r) +42270440/5133*G(18,20,20,r) +113480/59*G(19,20,20,r) +17640/61*G(20,20,20,r) +21*G(21,20,20,r) R(21,21,r) = +22/43*G(0,22,22,r) +2898/473*G(1,22,22,r) +18200/473*G(2,22,22,r) +1815450/10879*G(3,22,22,r) +284299470/511313*G(4,22,22,r) +768337542/511313*G(5,22,22,r) +157965088/46483*G(6,22,22,r) +2132528688/325381*G(7,22,22,r) +506818008/46483*G(8,22,22,r) +732070456/46483*G(9,22,22,r) +243991998432/12317995*G(10,22,22,r) +18638277658/859395*G(11,22,22,r) +1694388878/82203*G(12,22,22,r) +9857466/583*G(13,22,22,r) +6917520/583*G(14,22,22,r) +356713448/50721*G(15,22,22,r) +65076102/18821*G(16,22,22,r) +2350530/1711*G(17,22,22,r) +1526840/3599*G(18,22,22,r) +180810/1891*G(19,22,22,r) +14*G(20,22,22,r) +1*G(21,22,22,r) R(22,0,r) = -1/23*G(0,1,1,r) +6/23*G(1,1,1,r) -1038/805*G(2,1,1,r) +132/23*G(3,1,1,r) -9946/437*G(4,1,1,r) +163548/2185*G(5,1,1,r) -170854684/1077205*G(6,1,1,r) -179359752/1077205*G(7,1,1,r) +1428687546/392863*G(8,1,1,r) -7573576868/434217*G(9,1,1,r) +16467308/713*G(10,1,1,r) +182809432/899*G(11,1,1,r) -851994780/899*G(12,1,1,r) -1989132600/899*G(13,1,1,r) +17682607800/1147*G(14,1,1,r) +2962612848/37*G(15,1,1,r) +45496939554/259*G(16,1,1,r) +8468916588/37*G(17,1,1,r) +7911180860/41*G(18,1,1,r) +4384259880/41*G(19,1,1,r) +1625668044/43*G(20,1,1,r) +7759752*G(21,1,1,r) +705432*G(22,1,1,r) R(22,2,r) = +3/4025*G(0,3,3,r) -12/805*G(1,3,3,r) +1001/6555*G(2,3,3,r) -2456/2185*G(3,3,3,r) +4077898/646323*G(4,3,3,r) -133343496/5386025*G(5,3,3,r) +1095671577/33393355*G(6,3,3,r) +16779526192/41250615*G(7,3,3,r) -2537957994/723695*G(8,3,3,r) +183150968/20677*G(9,3,3,r) +240592066/4495*G(10,3,3,r) -1086935120/2697*G(11,3,3,r) -29263931580/33263*G(12,3,3,r) +11773313552/1147*G(13,3,3,r) +16050034305/259*G(14,3,3,r) +217021714272/1295*G(15,3,3,r) +419092814602/1517*G(16,3,3,r) +12417483672/41*G(17,3,3,r) +399869165982/1763*G(18,3,3,r) +4955155920/43*G(19,3,3,r) +190584212/5*G(20,3,3,r) +170714544/23*G(21,3,3,r) +646646*G(22,3,3,r) R(22,4,r) = -1/11799*G(0,5,5,r) +14/3933*G(1,5,5,r) -66668/1077205*G(2,5,5,r) +1318856/1938969*G(3,5,5,r) -104114153/20036013*G(4,5,5,r) +169967798/6678671*G(5,5,5,r) -62390328/1964315*G(6,5,5,r) -66532752/103385*G(7,5,5,r) +1087177182/227447*G(8,5,5,r) +58781996/24273*G(9,5,5,r) -55000009240/299367*G(10,5,5,r) +296801232/33263*G(11,5,5,r) +25488825271/3441*G(12,5,5,r) +1578504410/37*G(13,5,5,r) +195468258480/1517*G(14,5,5,r) +380558972640/1517*G(15,5,5,r) +594832515354/1763*G(16,5,5,r) +566954640252/1763*G(17,5,5,r) +84179368520/387*G(18,5,5,r) +77679820400/759*G(19,5,5,r) +34484161530/1081*G(20,5,5,r) +17782765/3*G(21,5,5,r) +497420*G(22,5,5,r) R(22,6,r) = +77/3231615*G(0,7,7,r) -1848/1077205*G(1,7,7,r) +300927/6678671*G(2,7,7,r) -157300/230299*G(3,7,7,r) +44341297/6678671*G(4,7,7,r) -72600528/1964315*G(5,7,7,r) +6712524/1137235*G(6,7,7,r) +370795152/227447*G(7,7,7,r) -241454238/33263*G(8,7,7,r) -6531769360/99789*G(9,7,7,r) +11169495909/33263*G(10,7,7,r) +5901147252/1147*G(11,7,7,r) +40663377755/1517*G(12,7,7,r) +127925323680/1517*G(13,7,7,r) +11878741302120/65231*G(14,7,7,r) +500256804960/1763*G(15,7,7,r) +573866387406/1763*G(16,7,7,r) +2999405157840/10879*G(17,7,7,r) +2027431261310/11891*G(18,7,7,r) +80935095150/1081*G(19,7,7,r) +44230005/2*G(20,7,7,r) +19697832/5*G(21,7,7,r) +319770*G(22,7,7,r) R(22,8,r) = -429/33393355*G(0,9,9,r) +9438/6678671*G(1,9,9,r) -3146/60605*G(2,9,9,r) +6818812/6678671*G(3,9,9,r) -153264748/12964479*G(4,9,9,r) +73602984/1137235*G(5,9,9,r) +1906827048/8415539*G(6,9,9,r) -845614736/166315*G(7,9,9,r) -113679375/14911*G(8,9,9,r) +11538109890/33263*G(9,9,9,r) +149694791246/47027*G(10,9,9,r) +22939136220/1517*G(11,9,9,r) +3121552698264/65231*G(12,9,9,r) +7154092465520/65231*G(13,9,9,r) +332915796720/1763*G(14,9,9,r) +110680435389888/446039*G(15,9,9,r) +127628389759260/511313*G(16,9,9,r) +2269190978964/11891*G(17,9,9,r) +117732511620/1081*G(18,9,9,r) +44907336*G(19,9,9,r) +63134568/5*G(20,9,9,r) +28139760/13*G(21,9,9,r) +170544*G(22,9,9,r) R(22,10,r) = +11/930465*G(0,11,11,r) -572/310155*G(1,11,11,r) +101829/1137235*G(2,11,11,r) -4430608/2047023*G(3,11,11,r) +231344228/8415539*G(4,11,11,r) -381258864/3825245*G(5,11,11,r) -3970680021/2162095*G(6,11,11,r) +4633362648/432419*G(7,11,11,r) +323899315695/1363783*G(8,11,11,r) +79783398940/47027*G(9,11,11,r) +487673983797/65231*G(10,11,11,r) +1529278759008/65231*G(11,11,11,r) +10860546510632/195693*G(12,11,11,r) +21095034666720/206701*G(13,11,11,r) +3096931248302580/20963833*G(14,11,11,r) +86356027597216/511313*G(15,11,11,r) +164114183058/1081*G(16,11,11,r) +572889955176/5405*G(17,11,11,r) +393663166/7*G(18,11,11,r) +284458272/13*G(19,11,11,r) +4050102168/689*G(20,11,11,r) +8754592/9*G(21,11,11,r) +74613*G(22,11,11,r) R(22,12,r) = -13/741675*G(0,13,13,r) +182/49445*G(1,13,13,r) -1237736/5488395*G(2,13,13,r) +34630768/5488395*G(3,13,13,r) -358591047/4756609*G(4,13,13,r) -2430932238/10810475*G(5,13,13,r) +549015627916/53187537*G(6,13,13,r) +169125827688/1363783*G(7,13,13,r) +1539243420057/2022161*G(8,13,13,r) +206073027090/65231*G(9,13,13,r) +3182479920048/326155*G(10,13,13,r) +7360913666053792/313565417*G(11,13,13,r) +17945205396016444/398312827*G(12,13,13,r) +1463369844566448/20963833*G(13,13,13,r) +313756781931360/3579191*G(14,13,13,r) +26463315487776/297275*G(15,13,13,r) +2742850355418/37835*G(16,13,13,r) +21220632828/455*G(17,13,13,r) +79727179536/3445*G(18,13,13,r) +5878238240/689*G(19,13,13,r) +10981677/5*G(20,13,13,r) +351747*G(21,13,13,r) +26334*G(22,13,13,r) R(22,14,r) = +15/365893*G(0,15,15,r) -4080/365893*G(1,15,15,r) +27444987/33296263*G(2,15,15,r) -115524180/4756609*G(3,15,15,r) +2645351095/17729179*G(4,15,15,r) +96811843800/17729179*G(5,15,15,r) +2963269610910/58642669*G(6,15,15,r) +566595340920/2022161*G(7,15,15,r) +72284850225/65231*G(8,15,15,r) +671268283524000/199541629*G(9,15,15,r) +10911164798090700/1339779509*G(10,15,15,r) +6396765679875168/398312827*G(11,15,15,r) +23781515972760/911471*G(12,15,15,r) +17940847722560/511313*G(13,15,15,r) +3249285018960/83237*G(14,15,15,r) +3515492402784/98371*G(15,15,15,r) +899473065882/33761*G(16,15,15,r) +54804117408/3445*G(17,15,15,r) +5111744705/689*G(18,15,15,r) +2600150*G(19,15,15,r) +1286145/2*G(20,15,15,r) +2896740/29*G(21,15,15,r) +7315*G(22,15,15,r) R(22,16,r) = -17/111111*G(0,17,17,r) +1938/37037*G(1,17,17,r) -953610/216931*G(2,17,17,r) +2053900/19721*G(3,17,17,r) +40941150/20683*G(4,17,17,r) +1031791500/65231*G(5,17,17,r) +5322379860/65231*G(6,17,17,r) +35833385199600/115524101*G(7,17,17,r) +456553658104200/493602977*G(8,17,17,r) +157871634900280/70514711*G(9,17,17,r) +8551850479128/1905803*G(10,17,17,r) +789454830673392/104819165*G(11,17,17,r) +114286698133816/10737573*G(12,17,17,r) +1959456786640/154583*G(13,17,17,r) +462841380608400/36495641*G(14,17,17,r) +5359957370272/506415*G(15,17,17,r) +25089233981/3445*G(16,17,17,r) +2797299510/689*G(17,17,17,r) +176902730/99*G(18,17,17,r) +17315700/29*G(19,17,17,r) +243258330/1711*G(20,17,17,r) +64372/3*G(21,17,17,r) +1540*G(22,17,17,r) R(22,18,r) = +19/19721*G(0,19,19,r) -7980/19721*G(1,19,19,r) +28270473/848003*G(2,19,19,r) +421852200/848003*G(3,19,19,r) +236528550/65231*G(4,19,19,r) +292470325560/16503443*G(5,19,19,r) +50535500237775/775661821*G(6,19,19,r) +13452664394016/70514711*G(7,19,19,r) +32410648013220/70514711*G(8,19,19,r) +1770343840048/1905803*G(9,19,19,r) +106261183109796/66703105*G(10,19,19,r) +758933172192/325381*G(11,19,19,r) +836937726456/286465*G(12,19,19,r) +2328643135456/744809*G(13,19,19,r) +13721746401/4823*G(14,19,19,r) +7522328912/3445*G(15,19,19,r) +10580021655/7579*G(16,19,19,r) +232911348/319*G(17,19,19,r) +520738415/1711*G(18,19,19,r) +166319160/1711*G(19,19,19,r) +1361766/61*G(20,19,19,r) +101640/31*G(21,19,19,r) +231*G(22,19,19,r) R(22,20,r) = -21/1763*G(0,21,21,r) +10626/1763*G(1,21,21,r) +141220/1763*G(2,21,21,r) +244740600/446039*G(3,21,21,r) +53862715725/20963833*G(4,21,21,r) +8939187621/975062*G(5,21,21,r) +50208506316/1905803*G(6,21,21,r) +599793439136/9529015*G(7,21,21,r) +1700681175108/13340621*G(8,21,21,r) +2954580047304/13340621*G(9,21,21,r) +28651773506928/86225965*G(10,21,21,r) +371136106016/859395*G(11,21,21,r) +139267548563/286465*G(12,21,21,r) +75159839/159*G(13,21,21,r) +230125644/583*G(14,21,21,r) +4743495312/16907*G(15,21,21,r) +9461451337/56463*G(16,21,21,r) +141280542/1711*G(17,21,21,r) +3412734780/104371*G(18,21,21,r) +18917640/1891*G(19,21,21,r) +68803/31*G(20,21,21,r) +2541/8*G(21,21,21,r) +22*G(22,21,21,r) R(22,22,r) = +23/45*G(0,23,23,r) +440/69*G(1,23,23,r) +45045/1081*G(2,23,23,r) +203203/1081*G(3,23,23,r) +2818365/4324*G(4,23,23,r) +49603224/27025*G(5,23,23,r) +70271234/16215*G(6,23,23,r) +4303507296/491855*G(7,23,23,r) +30662489484/2005255*G(8,23,23,r) +36047657888/1546911*G(9,23,23,r) +400722969647/12890925*G(10,23,23,r) +10408388822/286465*G(11,23,23,r) +177232627/4770*G(12,23,23,r) +763463624/23055*G(13,23,23,r) +2317657430/90683*G(14,23,23,r) +1302899312/76995*G(15,23,23,r) +990032043/104371*G(16,23,23,r) +14299467336/3235501*G(17,23,23,r) +28371959/17019*G(18,23,23,r) +182105/372*G(19,23,23,r) +109263/1040*G(20,23,23,r) +44/3*G(21,23,23,r) +1*G(22,23,23,r) Linearization coefficients: m= 0: R(0,0,r)*R(0,0,r) = +1*R(0,0,r) R(0,0,r)*R(2,0,r) = +1*R(2,0,r) R(0,0,r)*R(4,0,r) = +1*R(4,0,r) R(0,0,r)*R(6,0,r) = +1*R(6,0,r) R(0,0,r)*R(8,0,r) = +1*R(8,0,r) R(2,0,r)*R(2,0,r) = +1/3*R(0,0,r) +2/3*R(4,0,r) R(2,0,r)*R(4,0,r) = +2/5*R(2,0,r) +3/5*R(6,0,r) R(2,0,r)*R(6,0,r) = +3/7*R(4,0,r) +4/7*R(8,0,r) R(2,0,r)*R(8,0,r) = +4/9*R(6,0,r) +5/9*R(10,0,r) R(4,0,r)*R(4,0,r) = +1/5*R(0,0,r) +2/7*R(4,0,r) +18/35*R(8,0,r) R(4,0,r)*R(6,0,r) = +9/35*R(2,0,r) +4/15*R(6,0,r) +10/21*R(10,0,r) R(4,0,r)*R(8,0,r) = +2/7*R(4,0,r) +20/77*R(8,0,r) +5/11*R(12,0,r) R(6,0,r)*R(6,0,r) = +1/7*R(0,0,r) +4/21*R(4,0,r) +18/77*R(8,0,r) +100/231*R(12,0,r) R(6,0,r)*R(8,0,r) = +4/21*R(2,0,r) +2/11*R(6,0,r) +20/91*R(10,0,r) +175/429*R(14,0,r) R(8,0,r)*R(8,0,r) = +1/9*R(0,0,r) +100/693*R(4,0,r) +162/1001*R(8,0,r) +20/99*R(12,0,r) +490/1287*R(16,0,r) m= 1: R(1,1,r)*R(1,1,r) = +1*R(2,2,r) R(1,1,r)*R(3,1,r) = +1/4*R(2,2,r) +3/4*R(4,2,r) R(1,1,r)*R(5,1,r) = +1/3*R(4,2,r) +2/3*R(6,2,r) R(1,1,r)*R(7,1,r) = +3/8*R(6,2,r) +5/8*R(8,2,r) R(1,1,r)*R(9,1,r) = +2/5*R(8,2,r) +3/5*R(10,2,r) R(3,1,r)*R(3,1,r) = +2/5*R(2,2,r) +3/5*R(6,2,r) R(3,1,r)*R(5,1,r) = +3/20*R(2,2,r) +25/84*R(4,2,r) +1/60*R(6,2,r) +15/28*R(8,2,r) R(3,1,r)*R(7,1,r) = +3/14*R(4,2,r) +1/4*R(6,2,r) +1/28*R(8,2,r) +1/2*R(10,2,r) R(3,1,r)*R(9,1,r) = +1/4*R(6,2,r) +49/220*R(8,2,r) +1/20*R(10,2,r) +21/44*R(12,2,r) R(5,1,r)*R(5,1,r) = +9/35*R(2,2,r) +4/15*R(6,2,r) +10/21*R(10,2,r) R(5,1,r)*R(7,1,r) = +3/28*R(2,2,r) +7/36*R(4,2,r) +1/72*R(6,2,r) +21/88*R(8,2,r) +1/252*R(10,2,r) +175/396*R(12,2,r) R(5,1,r)*R(9,1,r) = +10/63*R(4,2,r) +16/99*R(6,2,r) +12/385*R(8,2,r) +128/585*R(10,2,r) +1/99*R(12,2,r) +60/143*R(14,2,r) R(7,1,r)*R(7,1,r) = +4/21*R(2,2,r) +2/11*R(6,2,r) +20/91*R(10,2,r) +175/429*R(14,2,r) R(7,1,r)*R(9,1,r) = +1/12*R(2,2,r) +45/308*R(4,2,r) +1/88*R(6,2,r) +6561/40040*R(8,2,r) +1/260*R(10,2,r) +9/44*R(12,2,r) +5/3432*R(14,2,r) +441/1144*R(16,2,r) R(9,1,r)*R(9,1,r) = +5/33*R(2,2,r) +20/143*R(6,2,r) +2/13*R(10,2,r) +1400/7293*R(14,2,r) +882/2431*R(18,2,r) m= 2: R(2,2,r)*R(2,2,r) = +1*R(4,4,r) R(2,2,r)*R(4,2,r) = +1/3*R(4,4,r) +2/3*R(6,4,r) R(2,2,r)*R(6,2,r) = +1/21*R(4,4,r) +5/12*R(6,4,r) +15/28*R(8,4,r) R(2,2,r)*R(8,2,r) = +1/12*R(6,4,r) +9/20*R(8,4,r) +7/15*R(10,4,r) R(2,2,r)*R(10,2,r) = +6/55*R(8,4,r) +7/15*R(10,4,r) +14/33*R(12,4,r) R(4,2,r)*R(4,2,r) = +3/7*R(4,4,r) +4/7*R(8,4,r) R(4,2,r)*R(6,2,r) = +3/14*R(4,4,r) +1/4*R(6,4,r) +1/28*R(8,4,r) +1/2*R(10,4,r) R(4,2,r)*R(8,2,r) = +5/126*R(4,4,r) +49/180*R(6,4,r) +243/1540*R(8,4,r) +7/90*R(10,4,r) +224/495*R(12,4,r) R(4,2,r)*R(10,2,r) = +4/55*R(6,4,r) +16/55*R(8,4,r) +7/65*R(10,4,r) +6/55*R(12,4,r) +60/143*R(14,4,r) R(6,2,r)*R(6,2,r) = +2/7*R(4,4,r) +20/77*R(8,4,r) +5/11*R(12,4,r) R(6,2,r)*R(8,2,r) = +10/63*R(4,4,r) +16/99*R(6,4,r) +12/385*R(8,4,r) +128/585*R(10,4,r) +1/99*R(12,4,r) +60/143*R(14,4,r) R(6,2,r)*R(10,2,r) = +5/154*R(4,4,r) +9/44*R(6,4,r) +1849/20020*R(8,4,r) +9/130*R(10,4,r) +2/11*R(12,4,r) +15/572*R(14,4,r) +225/572*R(16,4,r) R(8,2,r)*R(8,2,r) = +50/231*R(4,4,r) +180/1001*R(8,4,r) +7/33*R(12,4,r) +56/143*R(16,4,r) R(8,2,r)*R(10,2,r) = +25/198*R(4,4,r) +625/5148*R(6,4,r) +15/572*R(8,4,r) +35/234*R(10,4,r) +1/99*R(12,4,r) +1875/9724*R(14,4,r) +7/1716*R(16,4,r) +245/663*R(18,4,r) R(10,2,r)*R(10,2,r) = +25/143*R(4,4,r) +20/143*R(8,4,r) +28/187*R(12,4,r) +504/2717*R(16,4,r) +1470/4199*R(20,4,r) m= 3: R(3,3,r)*R(3,3,r) = +1*R(6,6,r) R(3,3,r)*R(5,3,r) = +3/8*R(6,6,r) +5/8*R(8,6,r) R(3,3,r)*R(7,3,r) = +1/12*R(6,6,r) +9/20*R(8,6,r) +7/15*R(10,6,r) R(3,3,r)*R(9,3,r) = +1/120*R(6,6,r) +63/440*R(8,6,r) +7/15*R(10,6,r) +21/55*R(12,6,r) R(3,3,r)*R(11,3,r) = +1/55*R(8,6,r) +12/65*R(10,6,r) +36/77*R(12,6,r) +30/91*R(14,6,r) R(5,3,r)*R(5,3,r) = +4/9*R(6,6,r) +5/9*R(10,6,r) R(5,3,r)*R(7,3,r) = +1/4*R(6,6,r) +49/220*R(8,6,r) +1/20*R(10,6,r) +21/44*R(12,6,r) R(5,3,r)*R(9,3,r) = +4/55*R(6,6,r) +16/55*R(8,6,r) +7/65*R(10,6,r) +6/55*R(12,6,r) +60/143*R(14,6,r) R(5,3,r)*R(11,3,r) = +7/792*R(6,6,r) +729/5720*R(8,6,r) +1156/4095*R(10,6,r) +4/77*R(12,6,r) +1215/8008*R(14,6,r) +275/728*R(16,6,r) R(7,3,r)*R(7,3,r) = +10/33*R(6,6,r) +10/39*R(10,6,r) +63/143*R(14,6,r) R(7,3,r)*R(9,3,r) = +25/132*R(6,6,r) +81/572*R(8,6,r) +7/156*R(10,6,r) +9/44*R(12,6,r) +9/572*R(14,6,r) +21/52*R(16,6,r) R(7,3,r)*R(11,3,r) = +35/572*R(6,6,r) +125/572*R(8,6,r) +5/91*R(10,6,r) +15/154*R(12,6,r) +10443/68068*R(14,6,r) +15/364*R(16,6,r) +165/442*R(18,6,r) R(9,3,r)*R(9,3,r) = +100/429*R(6,6,r) +7/39*R(10,6,r) +504/2431*R(14,6,r) +84/221*R(18,6,r) R(9,3,r)*R(11,3,r) = +175/1144*R(6,6,r) +11/104*R(8,6,r) +1/26*R(10,6,r) +33/238*R(12,6,r) +2187/136136*R(14,6,r) +363/1976*R(16,6,r) +3/442*R(18,6,r) +231/646*R(20,6,r) R(11,3,r)*R(11,3,r) = +245/1287*R(6,6,r) +280/1989*R(10,6,r) +6804/46189*R(14,6,r) +40/221*R(18,6,r) +110/323*R(22,6,r) m= 4: R(4,4,r)*R(4,4,r) = +1*R(8,8,r) R(4,4,r)*R(6,4,r) = +2/5*R(8,8,r) +3/5*R(10,8,r) R(4,4,r)*R(8,4,r) = +6/55*R(8,8,r) +7/15*R(10,8,r) +14/33*R(12,8,r) R(4,4,r)*R(10,4,r) = +1/55*R(8,8,r) +12/65*R(10,8,r) +36/77*R(12,8,r) +30/91*R(14,8,r) R(4,4,r)*R(12,4,r) = +1/715*R(8,8,r) +18/455*R(10,8,r) +18/77*R(12,8,r) +165/364*R(14,8,r) +99/364*R(16,8,r) R(6,4,r)*R(6,4,r) = +5/11*R(8,8,r) +6/11*R(12,8,r) R(6,4,r)*R(8,4,r) = +3/11*R(8,8,r) +8/39*R(10,8,r) +2/33*R(12,8,r) +6/13*R(14,8,r) R(6,4,r)*R(10,4,r) = +14/143*R(8,8,r) +27/91*R(10,8,r) +6/77*R(12,8,r) +12/91*R(14,8,r) +36/91*R(16,8,r) R(6,4,r)*R(12,4,r) = +20/1001*R(8,8,r) +15/91*R(10,8,r) +81/308*R(12,8,r) +75/3094*R(14,8,r) +33/182*R(16,8,r) +165/476*R(18,8,r) R(8,4,r)*R(8,4,r) = +45/143*R(8,8,r) +14/55*R(12,8,r) +28/65*R(16,8,r) R(8,4,r)*R(10,4,r) = +30/143*R(8,8,r) +5/39*R(10,8,r) +64/1155*R(12,8,r) +300/1547*R(14,8,r) +4/195*R(16,8,r) +20/51*R(18,8,r) R(8,4,r)*R(12,4,r) = +12/143*R(8,8,r) +121/546*R(10,8,r) +529/15708*R(12,8,r) +363/3094*R(14,8,r) +1369/10374*R(16,8,r) +11/204*R(18,8,r) +231/646*R(20,8,r) R(10,4,r)*R(10,4,r) = +35/143*R(8,8,r) +168/935*R(12,8,r) +252/1235*R(16,8,r) +120/323*R(20,8,r) R(10,4,r)*R(12,4,r) = +49/286*R(8,8,r) +21/221*R(10,8,r) +9/187*R(12,8,r) +2187/16796*R(14,8,r) +21/988*R(16,8,r) +3/17*R(18,8,r) +3/323*R(20,8,r) +225/646*R(22,8,r) R(12,4,r)*R(12,4,r) = +490/2431*R(8,8,r) +504/3553*R(12,8,r) +36/247*R(16,8,r) +1320/7429*R(20,8,r) +2475/7429*R(24,8,r) m= 5: R(5,5,r)*R(5,5,r) = +1*R(10,10,r) R(5,5,r)*R(7,5,r) = +5/12*R(10,10,r) +7/12*R(12,10,r) R(5,5,r)*R(9,5,r) = +5/39*R(10,10,r) +10/21*R(12,10,r) +36/91*R(14,10,r) R(5,5,r)*R(11,5,r) = +5/182*R(10,10,r) +3/14*R(12,10,r) +675/1456*R(14,10,r) +33/112*R(16,10,r) R(5,5,r)*R(13,5,r) = +1/273*R(10,10,r) +5/84*R(12,10,r) +825/3094*R(14,10,r) +55/126*R(16,10,r) +143/612*R(18,10,r) R(7,5,r)*R(7,5,r) = +6/13*R(10,10,r) +7/13*R(14,10,r) R(7,5,r)*R(9,5,r) = +15/52*R(10,10,r) +27/140*R(12,10,r) +25/364*R(14,10,r) +9/20*R(16,10,r) R(7,5,r)*R(11,5,r) = +32/273*R(10,10,r) +25/84*R(12,10,r) +729/12376*R(14,10,r) +25/168*R(16,10,r) +77/204*R(18,10,r) R(7,5,r)*R(13,5,r) = +45/1456*R(10,10,r) +363/1904*R(12,10,r) +9025/37128*R(14,10,r) +11/1064*R(16,10,r) +55/272*R(18,10,r) +5005/15504*R(20,10,r) R(9,5,r)*R(9,5,r) = +21/65*R(10,10,r) +56/221*R(14,10,r) +36/85*R(18,10,r) R(9,5,r)*R(11,5,r) = +35/156*R(10,10,r) +121/1020*R(12,10,r) +225/3536*R(14,10,r) +847/4560*R(16,10,r) +5/204*R(18,10,r) +495/1292*R(20,10,r) R(9,5,r)*R(13,5,r) = +45/442*R(10,10,r) +15/68*R(12,10,r) +529/25194*R(14,10,r) +5/38*R(16,10,r) +55/476*R(18,10,r) +125/1938*R(20,10,r) +780/2261*R(22,10,r) R(11,5,r)*R(11,5,r) = +56/221*R(10,10,r) +756/4199*R(14,10,r) +24/119*R(18,10,r) +825/2261*R(22,10,r) R(11,5,r)*R(13,5,r) = +245/1326*R(10,10,r) +169/1938*R(12,10,r) +1875/33592*R(14,10,r) +169/1368*R(16,10,r) +55/2142*R(18,10,r) +2535/14858*R(20,10,r) +625/54264*R(22,10,r) +3575/10488*R(24,10,r) R(13,5,r)*R(13,5,r) = +882/4199*R(10,10,r) +600/4199*R(14,10,r) +396/2737*R(18,10,r) +396/2261*R(22,10,r) +143/437*R(26,10,r) m= 6: R(6,6,r)*R(6,6,r) = +1*R(12,12,r) R(6,6,r)*R(8,6,r) = +3/7*R(12,12,r) +4/7*R(14,12,r) R(6,6,r)*R(10,6,r) = +1/7*R(12,12,r) +27/56*R(14,12,r) +3/8*R(16,12,r) R(6,6,r)*R(12,6,r) = +1/28*R(12,12,r) +225/952*R(14,12,r) +11/24*R(16,12,r) +55/204*R(18,12,r) R(6,6,r)*R(14,6,r) = +3/476*R(12,12,r) +55/714*R(14,12,r) +11/38*R(16,12,r) +143/340*R(18,12,r) +1001/4845*R(20,12,r) R(8,6,r)*R(8,6,r) = +7/15*R(12,12,r) +8/15*R(16,12,r) R(8,6,r)*R(10,6,r) = +3/10*R(12,12,r) +25/136*R(14,12,r) +3/40*R(16,12,r) +15/34*R(18,12,r) R(8,6,r)*R(12,6,r) = +9/68*R(12,12,r) +121/408*R(14,12,r) +7/152*R(16,12,r) +11/68*R(18,12,r) +352/969*R(20,12,r) R(8,6,r)*R(14,6,r) = +25/612*R(12,12,r) +135/646*R(14,12,r) +77/342*R(16,12,r) +11/3060*R(18,12,r) +351/1615*R(20,12,r) +52/171*R(22,12,r) R(10,6,r)*R(10,6,r) = +28/85*R(12,12,r) +24/95*R(16,12,r) +135/323*R(20,12,r) R(10,6,r)*R(12,6,r) = +4/17*R(12,12,r) +36/323*R(14,12,r) +4/57*R(16,12,r) +64/357*R(18,12,r) +9/323*R(20,12,r) +50/133*R(22,12,r) R(10,6,r)*R(14,6,r) = +75/646*R(12,12,r) +845/3876*R(14,12,r) +1/76*R(16,12,r) +169/1190*R(18,12,r) +11449/111435*R(20,12,r) +39/532*R(22,12,r) +585/1748*R(24,12,r) R(12,6,r)*R(12,6,r) = +84/323*R(12,12,r) +24/133*R(16,12,r) +1485/7429*R(20,12,r) +1100/3059*R(24,12,r) R(12,6,r)*R(14,6,r) = +63/323*R(12,12,r) +105/1292*R(14,12,r) +33/532*R(16,12,r) +231/1955*R(18,12,r) +2187/74290*R(20,12,r) +63/380*R(22,12,r) +165/12236*R(24,12,r) +77/230*R(26,12,r) R(14,6,r)*R(14,6,r) = +70/323*R(12,12,r) +440/3059*R(16,12,r) +5346/37145*R(20,12,r) +14300/82593*R(24,12,r) +1001/3105*R(28,12,r) m= 7: R(7,7,r)*R(7,7,r) = +1*R(14,14,r) R(7,7,r)*R(9,7,r) = +7/16*R(14,14,r) +9/16*R(16,14,r) R(7,7,r)*R(11,7,r) = +21/136*R(14,14,r) +35/72*R(16,14,r) +55/153*R(18,14,r) R(7,7,r)*R(13,7,r) = +35/816*R(14,14,r) +77/304*R(16,14,r) +77/170*R(18,14,r) +143/570*R(20,14,r) R(7,7,r)*R(15,7,r) = +35/3876*R(14,14,r) +7/76*R(16,14,r) +26/85*R(18,14,r) +1274/3135*R(20,14,r) +39/209*R(22,14,r) R(9,7,r)*R(9,7,r) = +8/17*R(14,14,r) +9/17*R(18,14,r) R(9,7,r)*R(11,7,r) = +21/68*R(14,14,r) +121/684*R(16,14,r) +49/612*R(18,14,r) +33/76*R(20,14,r) R(9,7,r)*R(13,7,r) = +140/969*R(14,14,r) +28/95*R(16,14,r) +22/595*R(18,14,r) +49/285*R(20,14,r) +234/665*R(22,14,r) R(9,7,r)*R(15,7,r) = +385/7752*R(14,14,r) +169/760*R(16,14,r) +196/935*R(18,14,r) +52/72105*R(20,14,r) +1911/8360*R(22,14,r) +585/2024*R(24,14,r) R(11,7,r)*R(11,7,r) = +108/323*R(14,14,r) +30/119*R(18,14,r) +55/133*R(22,14,r) R(11,7,r)*R(13,7,r) = +315/1292*R(14,14,r) +169/1596*R(16,14,r) +77/1020*R(18,14,r) +1521/8740*R(20,14,r) +7/228*R(22,14,r) +715/1932*R(24,14,r) R(11,7,r)*R(15,7,r) = +165/1292*R(14,14,r) +49/228*R(16,14,r) +3698/451605*R(18,14,r) +7203/48070*R(20,14,r) +1625/17556*R(22,14,r) +245/3036*R(24,14,r) +15/46*R(26,14,r) R(13,7,r)*R(13,7,r) = +600/2261*R(14,14,r) +495/2737*R(18,14,r) +132/665*R(22,14,r) +286/805*R(26,14,r) R(13,7,r)*R(15,7,r) = +525/2584*R(14,14,r) +1875/24472*R(16,14,r) +105/1564*R(18,14,r) +2187/19228*R(20,14,r) +273/8360*R(22,14,r) +625/3864*R(24,14,r) +7/460*R(26,14,r) +91/276*R(28,14,r) R(15,7,r)*R(15,7,r) = +1650/7429*R(14,14,r) +396/2737*R(18,14,r) +286/1995*R(22,14,r) +572/3335*R(26,14,r) +637/2001*R(30,14,r) m= 8: R(8,8,r)*R(8,8,r) = +1*R(16,16,r) R(8,8,r)*R(10,8,r) = +4/9*R(16,16,r) +5/9*R(18,16,r) R(8,8,r)*R(12,8,r) = +28/171*R(16,16,r) +22/45*R(18,16,r) +33/95*R(20,16,r) R(8,8,r)*R(14,8,r) = +14/285*R(16,16,r) +4/15*R(18,16,r) +468/1045*R(20,16,r) +13/55*R(22,16,r) R(8,8,r)*R(16,8,r) = +2/171*R(16,16,r) +52/495*R(18,16,r) +7644/24035*R(20,16,r) +13/33*R(22,16,r) +130/759*R(24,16,r) R(10,8,r)*R(10,8,r) = +9/19*R(16,16,r) +10/19*R(20,16,r) R(10,8,r)*R(12,8,r) = +6/19*R(16,16,r) +6/35*R(18,16,r) +8/95*R(20,16,r) +3/7*R(22,16,r) R(10,8,r)*R(14,8,r) = +44/285*R(16,16,r) +338/1155*R(18,16,r) +729/24035*R(20,16,r) +208/1155*R(22,16,r) +260/759*R(24,16,r) R(10,8,r)*R(16,8,r) = +12/209*R(16,16,r) +294/1265*R(18,16,r) +429/2185*R(20,16,r) +60/253*R(24,16,r) +70/253*R(26,16,r) R(12,8,r)*R(12,8,r) = +45/133*R(16,16,r) +110/437*R(20,16,r) +66/161*R(24,16,r) R(12,8,r)*R(14,8,r) = +100/399*R(16,16,r) +7/69*R(18,16,r) +384/4807*R(20,16,r) +28/165*R(22,16,r) +16/483*R(24,16,r) +42/115*R(26,16,r) R(12,8,r)*R(16,8,r) = +60/437*R(16,16,r) +375/1771*R(18,16,r) +24/4807*R(20,16,r) +12/77*R(22,16,r) +64/759*R(24,16,r) +2/23*R(26,16,r) +22/69*R(28,16,r) R(14,8,r)*R(14,8,r) = +825/3059*R(16,16,r) +396/2185*R(20,16,r) +286/1449*R(24,16,r) +364/1035*R(28,16,r) R(14,8,r)*R(16,8,r) = +275/1311*R(16,16,r) +176/2415*R(18,16,r) +156/2185*R(20,16,r) +104/945*R(22,16,r) +22/621*R(24,16,r) +528/3335*R(26,16,r) +52/3105*R(28,16,r) +1274/3915*R(30,16,r) R(16,8,r)*R(16,8,r) = +99/437*R(16,16,r) +572/3933*R(20,16,r) +286/2001*R(24,16,r) +364/2139*R(28,16,r) +2548/8091*R(32,16,r) Bivariate Cartesian to spherical coordinates, X=r*cos(phi), Y=r*sin(phi): X = r*cos(phi) Y = r*sin(phi) X^2 = 1/2*r^2*cos(2*phi) +1/2*r^2 X*Y = 1/2*r^2*sin(2*phi) Y^2 = -1/2*r^2*cos(2*phi) +1/2*r^2 X^3 = 1/4*r^3*cos(3*phi) +3/4*r^3*cos(phi) X^2*Y = 1/4*r^3*sin(3*phi) +1/4*r^3*sin(phi) X*Y^2 = -1/4*r^3*cos(3*phi) +1/4*r^3*cos(phi) Y^3 = -1/4*r^3*sin(3*phi) +3/4*r^3*sin(phi) X^4 = 1/8*r^4*cos(4*phi) +1/2*r^4*cos(2*phi) +3/8*r^4 X^3*Y = 1/8*r^4*sin(4*phi) +1/4*r^4*sin(2*phi) X^2*Y^2 = -1/8*r^4*cos(4*phi) +1/8*r^4 X*Y^3 = -1/8*r^4*sin(4*phi) +1/4*r^4*sin(2*phi) Y^4 = 1/8*r^4*cos(4*phi) -1/2*r^4*cos(2*phi) +3/8*r^4 X^5 = 1/16*r^5*cos(5*phi) +5/16*r^5*cos(3*phi) +5/8*r^5*cos(phi) X^4*Y = 1/16*r^5*sin(5*phi) +3/16*r^5*sin(3*phi) +1/8*r^5*sin(phi) X^3*Y^2 = -1/16*r^5*cos(5*phi) -1/16*r^5*cos(3*phi) +1/8*r^5*cos(phi) X^2*Y^3 = -1/16*r^5*sin(5*phi) +1/16*r^5*sin(3*phi) +1/8*r^5*sin(phi) X*Y^4 = 1/16*r^5*cos(5*phi) -3/16*r^5*cos(3*phi) +1/8*r^5*cos(phi) Y^5 = 1/16*r^5*sin(5*phi) -5/16*r^5*sin(3*phi) +5/8*r^5*sin(phi) X^6 = 1/32*r^6*cos(6*phi) +3/16*r^6*cos(4*phi) +15/32*r^6*cos(2*phi) +5/16*r^6 X^5*Y = 1/32*r^6*sin(6*phi) +1/8*r^6*sin(4*phi) +5/32*r^6*sin(2*phi) X^4*Y^2 = -1/32*r^6*cos(6*phi) -1/16*r^6*cos(4*phi) +1/32*r^6*cos(2*phi) +1/16*r^6 X^3*Y^3 = -1/32*r^6*sin(6*phi) +3/32*r^6*sin(2*phi) X^2*Y^4 = 1/32*r^6*cos(6*phi) -1/16*r^6*cos(4*phi) -1/32*r^6*cos(2*phi) +1/16*r^6 X*Y^5 = 1/32*r^6*sin(6*phi) -1/8*r^6*sin(4*phi) +5/32*r^6*sin(2*phi) Y^6 = -1/32*r^6*cos(6*phi) +3/16*r^6*cos(4*phi) -15/32*r^6*cos(2*phi) +5/16*r^6 X^7 = 1/64*r^7*cos(7*phi) +7/64*r^7*cos(5*phi) +21/64*r^7*cos(3*phi) +35/64*r^7*cos(phi) X^6*Y = 1/64*r^7*sin(7*phi) +5/64*r^7*sin(5*phi) +9/64*r^7*sin(3*phi) +5/64*r^7*sin(phi) X^5*Y^2 = -1/64*r^7*cos(7*phi) -3/64*r^7*cos(5*phi) -1/64*r^7*cos(3*phi) +5/64*r^7*cos(phi) X^4*Y^3 = -1/64*r^7*sin(7*phi) -1/64*r^7*sin(5*phi) +3/64*r^7*sin(3*phi) +3/64*r^7*sin(phi) X^3*Y^4 = 1/64*r^7*cos(7*phi) -1/64*r^7*cos(5*phi) -3/64*r^7*cos(3*phi) +3/64*r^7*cos(phi) X^2*Y^5 = 1/64*r^7*sin(7*phi) -3/64*r^7*sin(5*phi) +1/64*r^7*sin(3*phi) +5/64*r^7*sin(phi) X*Y^6 = -1/64*r^7*cos(7*phi) +5/64*r^7*cos(5*phi) -9/64*r^7*cos(3*phi) +5/64*r^7*cos(phi) Y^7 = -1/64*r^7*sin(7*phi) +7/64*r^7*sin(5*phi) -21/64*r^7*sin(3*phi) +35/64*r^7*sin(phi) X^8 = 1/128*r^8*cos(8*phi) +1/16*r^8*cos(6*phi) +7/32*r^8*cos(4*phi) +7/16*r^8*cos(2*phi) +35/128*r^8 X^7*Y = 1/128*r^8*sin(8*phi) +3/64*r^8*sin(6*phi) +7/64*r^8*sin(4*phi) +7/64*r^8*sin(2*phi) X^6*Y^2 = -1/128*r^8*cos(8*phi) -1/32*r^8*cos(6*phi) -1/32*r^8*cos(4*phi) +1/32*r^8*cos(2*phi) +5/128*r^8 X^5*Y^3 = -1/128*r^8*sin(8*phi) -1/64*r^8*sin(6*phi) +1/64*r^8*sin(4*phi) +3/64*r^8*sin(2*phi) X^4*Y^4 = 1/128*r^8*cos(8*phi) -1/32*r^8*cos(4*phi) +3/128*r^8 X^3*Y^5 = 1/128*r^8*sin(8*phi) -1/64*r^8*sin(6*phi) -1/64*r^8*sin(4*phi) +3/64*r^8*sin(2*phi) X^2*Y^6 = -1/128*r^8*cos(8*phi) +1/32*r^8*cos(6*phi) -1/32*r^8*cos(4*phi) -1/32*r^8*cos(2*phi) +5/128*r^8 X*Y^7 = -1/128*r^8*sin(8*phi) +3/64*r^8*sin(6*phi) -7/64*r^8*sin(4*phi) +7/64*r^8*sin(2*phi) Y^8 = 1/128*r^8*cos(8*phi) -1/16*r^8*cos(6*phi) +7/32*r^8*cos(4*phi) -7/16*r^8*cos(2*phi) +35/128*r^8 X^9 = 1/256*r^9*cos(9*phi) +9/256*r^9*cos(7*phi) +9/64*r^9*cos(5*phi) +21/64*r^9*cos(3*phi) +63/128*r^9*cos(phi) X^8*Y = 1/256*r^9*sin(9*phi) +7/256*r^9*sin(7*phi) +5/64*r^9*sin(5*phi) +7/64*r^9*sin(3*phi) +7/128*r^9*sin(phi) X^7*Y^2 = -1/256*r^9*cos(9*phi) -5/256*r^9*cos(7*phi) -1/32*r^9*cos(5*phi) +7/128*r^9*cos(phi) X^6*Y^3 = -1/256*r^9*sin(9*phi) -3/256*r^9*sin(7*phi) +1/32*r^9*sin(3*phi) +3/128*r^9*sin(phi) X^5*Y^4 = 1/256*r^9*cos(9*phi) +1/256*r^9*cos(7*phi) -1/64*r^9*cos(5*phi) -1/64*r^9*cos(3*phi) +3/128*r^9*cos(phi) X^4*Y^5 = 1/256*r^9*sin(9*phi) -1/256*r^9*sin(7*phi) -1/64*r^9*sin(5*phi) +1/64*r^9*sin(3*phi) +3/128*r^9*sin(phi) X^3*Y^6 = -1/256*r^9*cos(9*phi) +3/256*r^9*cos(7*phi) -1/32*r^9*cos(3*phi) +3/128*r^9*cos(phi) X^2*Y^7 = -1/256*r^9*sin(9*phi) +5/256*r^9*sin(7*phi) -1/32*r^9*sin(5*phi) +7/128*r^9*sin(phi) X*Y^8 = 1/256*r^9*cos(9*phi) -7/256*r^9*cos(7*phi) +5/64*r^9*cos(5*phi) -7/64*r^9*cos(3*phi) +7/128*r^9*cos(phi) Y^9 = 1/256*r^9*sin(9*phi) -9/256*r^9*sin(7*phi) +9/64*r^9*sin(5*phi) -21/64*r^9*sin(3*phi) +63/128*r^9*sin(phi) X^10 = 1/512*r^10*cos(10*phi) +5/256*r^10*cos(8*phi) +45/512*r^10*cos(6*phi) +15/64*r^10*cos(4*phi) +105/256*r^10*cos(2*phi) +63/256*r^10 X^9*Y = 1/512*r^10*sin(10*phi) +1/64*r^10*sin(8*phi) +27/512*r^10*sin(6*phi) +3/32*r^10*sin(4*phi) +21/256*r^10*sin(2*phi) X^8*Y^2 = -1/512*r^10*cos(10*phi) -3/256*r^10*cos(8*phi) -13/512*r^10*cos(6*phi) -1/64*r^10*cos(4*phi) +7/256*r^10*cos(2*phi) +7/256*r^10 X^7*Y^3 = -1/512*r^10*sin(10*phi) -1/128*r^10*sin(8*phi) -3/512*r^10*sin(6*phi) +1/64*r^10*sin(4*phi) +7/256*r^10*sin(2*phi) X^6*Y^4 = 1/512*r^10*cos(10*phi) +1/256*r^10*cos(8*phi) -3/512*r^10*cos(6*phi) -1/64*r^10*cos(4*phi) +1/256*r^10*cos(2*phi) +3/256*r^10 X^5*Y^5 = 1/512*r^10*sin(10*phi) -5/512*r^10*sin(6*phi) +5/256*r^10*sin(2*phi) X^4*Y^6 = -1/512*r^10*cos(10*phi) +1/256*r^10*cos(8*phi) +3/512*r^10*cos(6*phi) -1/64*r^10*cos(4*phi) -1/256*r^10*cos(2*phi) +3/256*r^10 X^3*Y^7 = -1/512*r^10*sin(10*phi) +1/128*r^10*sin(8*phi) -3/512*r^10*sin(6*phi) -1/64*r^10*sin(4*phi) +7/256*r^10*sin(2*phi) X^2*Y^8 = 1/512*r^10*cos(10*phi) -3/256*r^10*cos(8*phi) +13/512*r^10*cos(6*phi) -1/64*r^10*cos(4*phi) -7/256*r^10*cos(2*phi) +7/256*r^10 X*Y^9 = 1/512*r^10*sin(10*phi) -1/64*r^10*sin(8*phi) +27/512*r^10*sin(6*phi) -3/32*r^10*sin(4*phi) +21/256*r^10*sin(2*phi) Y^10 = -1/512*r^10*cos(10*phi) +5/256*r^10*cos(8*phi) -45/512*r^10*cos(6*phi) +15/64*r^10*cos(4*phi) -105/256*r^10*cos(2*phi) +63/256*r^10 X^11 = 1/1024*r^11*cos(11*phi) +11/1024*r^11*cos(9*phi) +55/1024*r^11*cos(7*phi) +165/1024*r^11*cos(5*phi) +165/512*r^11*cos(3*phi) +231/512*r^11*cos(phi) X^10*Y = 1/1024*r^11*sin(11*phi) +9/1024*r^11*sin(9*phi) +35/1024*r^11*sin(7*phi) +75/1024*r^11*sin(5*phi) +45/512*r^11*sin(3*phi) +21/512*r^11*sin(phi) X^9*Y^2 = -1/1024*r^11*cos(11*phi) -7/1024*r^11*cos(9*phi) -19/1024*r^11*cos(7*phi) -21/1024*r^11*cos(5*phi) +3/512*r^11*cos(3*phi) +21/512*r^11*cos(phi) X^8*Y^3 = -1/1024*r^11*sin(11*phi) -5/1024*r^11*sin(9*phi) -7/1024*r^11*sin(7*phi) +5/1024*r^11*sin(5*phi) +11/512*r^11*sin(3*phi) +7/512*r^11*sin(phi) X^7*Y^4 = 1/1024*r^11*cos(11*phi) +3/1024*r^11*cos(9*phi) -1/1024*r^11*cos(7*phi) -11/1024*r^11*cos(5*phi) -3/512*r^11*cos(3*phi) +7/512*r^11*cos(phi) X^6*Y^5 = 1/1024*r^11*sin(11*phi) +1/1024*r^11*sin(9*phi) -5/1024*r^11*sin(7*phi) -5/1024*r^11*sin(5*phi) +5/512*r^11*sin(3*phi) +5/512*r^11*sin(phi) X^5*Y^6 = -1/1024*r^11*cos(11*phi) +1/1024*r^11*cos(9*phi) +5/1024*r^11*cos(7*phi) -5/1024*r^11*cos(5*phi) -5/512*r^11*cos(3*phi) +5/512*r^11*cos(phi) X^4*Y^7 = -1/1024*r^11*sin(11*phi) +3/1024*r^11*sin(9*phi) +1/1024*r^11*sin(7*phi) -11/1024*r^11*sin(5*phi) +3/512*r^11*sin(3*phi) +7/512*r^11*sin(phi) X^3*Y^8 = 1/1024*r^11*cos(11*phi) -5/1024*r^11*cos(9*phi) +7/1024*r^11*cos(7*phi) +5/1024*r^11*cos(5*phi) -11/512*r^11*cos(3*phi) +7/512*r^11*cos(phi) X^2*Y^9 = 1/1024*r^11*sin(11*phi) -7/1024*r^11*sin(9*phi) +19/1024*r^11*sin(7*phi) -21/1024*r^11*sin(5*phi) -3/512*r^11*sin(3*phi) +21/512*r^11*sin(phi) X*Y^10 = -1/1024*r^11*cos(11*phi) +9/1024*r^11*cos(9*phi) -35/1024*r^11*cos(7*phi) +75/1024*r^11*cos(5*phi) -45/512*r^11*cos(3*phi) +21/512*r^11*cos(phi) Y^11 = -1/1024*r^11*sin(11*phi) +11/1024*r^11*sin(9*phi) -55/1024*r^11*sin(7*phi) +165/1024*r^11*sin(5*phi) -165/512*r^11*sin(3*phi) +231/512*r^11*sin(phi) X^12 = 1/2048*r^12*cos(12*phi) +3/512*r^12*cos(10*phi) +33/1024*r^12*cos(8*phi) +55/512*r^12*cos(6*phi) +495/2048*r^12*cos(4*phi) +99/256*r^12*cos(2*phi) +231/1024*r^12 X^11*Y = 1/2048*r^12*sin(12*phi) +5/1024*r^12*sin(10*phi) +11/512*r^12*sin(8*phi) +55/1024*r^12*sin(6*phi) +165/2048*r^12*sin(4*phi) +33/512*r^12*sin(2*phi) X^10*Y^2 = -1/2048*r^12*cos(12*phi) -1/256*r^12*cos(10*phi) -13/1024*r^12*cos(8*phi) -5/256*r^12*cos(6*phi) -15/2048*r^12*cos(4*phi) +3/128*r^12*cos(2*phi) +21/1024*r^12 X^9*Y^3 = -1/2048*r^12*sin(12*phi) -3/1024*r^12*sin(10*phi) -3/512*r^12*sin(8*phi) -1/1024*r^12*sin(6*phi) +27/2048*r^12*sin(4*phi) +9/512*r^12*sin(2*phi) X^8*Y^4 = 1/2048*r^12*cos(12*phi) +1/512*r^12*cos(10*phi) +1/1024*r^12*cos(8*phi) -3/512*r^12*cos(6*phi) -17/2048*r^12*cos(4*phi) +1/256*r^12*cos(2*phi) +7/1024*r^12 X^7*Y^5 = 1/2048*r^12*sin(12*phi) +1/1024*r^12*sin(10*phi) -1/512*r^12*sin(8*phi) -5/1024*r^12*sin(6*phi) +5/2048*r^12*sin(4*phi) +5/512*r^12*sin(2*phi) X^6*Y^6 = -1/2048*r^12*cos(12*phi) +3/1024*r^12*cos(8*phi) -15/2048*r^12*cos(4*phi) +5/1024*r^12 X^5*Y^7 = -1/2048*r^12*sin(12*phi) +1/1024*r^12*sin(10*phi) +1/512*r^12*sin(8*phi) -5/1024*r^12*sin(6*phi) -5/2048*r^12*sin(4*phi) +5/512*r^12*sin(2*phi) X^4*Y^8 = 1/2048*r^12*cos(12*phi) -1/512*r^12*cos(10*phi) +1/1024*r^12*cos(8*phi) +3/512*r^12*cos(6*phi) -17/2048*r^12*cos(4*phi) -1/256*r^12*cos(2*phi) +7/1024*r^12 X^3*Y^9 = 1/2048*r^12*sin(12*phi) -3/1024*r^12*sin(10*phi) +3/512*r^12*sin(8*phi) -1/1024*r^12*sin(6*phi) -27/2048*r^12*sin(4*phi) +9/512*r^12*sin(2*phi) X^2*Y^10 = -1/2048*r^12*cos(12*phi) +1/256*r^12*cos(10*phi) -13/1024*r^12*cos(8*phi) +5/256*r^12*cos(6*phi) -15/2048*r^12*cos(4*phi) -3/128*r^12*cos(2*phi) +21/1024*r^12 X*Y^11 = -1/2048*r^12*sin(12*phi) +5/1024*r^12*sin(10*phi) -11/512*r^12*sin(8*phi) +55/1024*r^12*sin(6*phi) -165/2048*r^12*sin(4*phi) +33/512*r^12*sin(2*phi) Y^12 = 1/2048*r^12*cos(12*phi) -3/512*r^12*cos(10*phi) +33/1024*r^12*cos(8*phi) -55/512*r^12*cos(6*phi) +495/2048*r^12*cos(4*phi) -99/256*r^12*cos(2*phi) +231/1024*r^12 radial polynomials in terms of Zernike polynomials R(n,m,r): m = 0 r^0 = +1*R(0,0,r) r^2 = +1/2*R(0,0,r) +1/2*R(2,0,r) r^4 = +1/3*R(0,0,r) +1/2*R(2,0,r) +1/6*R(4,0,r) r^6 = +1/4*R(0,0,r) +9/20*R(2,0,r) +1/4*R(4,0,r) +1/20*R(6,0,r) r^8 = +1/5*R(0,0,r) +2/5*R(2,0,r) +2/7*R(4,0,r) +1/10*R(6,0,r) +1/70*R(8,0,r) r^10 = +1/6*R(0,0,r) +5/14*R(2,0,r) +25/84*R(4,0,r) +5/36*R(6,0,r) +1/28*R(8,0,r) +1/252*R(10,0,r) r^12 = +1/7*R(0,0,r) +9/28*R(2,0,r) +25/84*R(4,0,r) +1/6*R(6,0,r) +9/154*R(8,0,r) +1/84*R(10,0,r) +1/924*R(12,0,r) r^14 = +1/8*R(0,0,r) +7/24*R(2,0,r) +7/24*R(4,0,r) +49/264*R(6,0,r) +7/88*R(8,0,r) +7/312*R(10,0,r) +1/264*R(12,0,r) +1/3432*R(14,0,r) r^16 = +1/9*R(0,0,r) +4/15*R(2,0,r) +28/99*R(4,0,r) +98/495*R(6,0,r) +14/143*R(8,0,r) +4/117*R(10,0,r) +4/495*R(12,0,r) +1/858*R(14,0,r) +1/12870*R(16,0,r) r^18 = +1/10*R(0,0,r) +27/110*R(2,0,r) +3/11*R(4,0,r) +147/715*R(6,0,r) +81/715*R(8,0,r) +3/65*R(10,0,r) +3/220*R(12,0,r) +27/9724*R(14,0,r) +1/2860*R(16,0,r) +1/48620*R(18,0,r) r^20 = +1/11*R(0,0,r) +5/22*R(2,0,r) +75/286*R(4,0,r) +30/143*R(6,0,r) +18/143*R(8,0,r) +3/52*R(10,0,r) +15/748*R(12,0,r) +25/4862*R(14,0,r) +5/5434*R(16,0,r) +1/9724*R(18,0,r) +1/184756*R(20,0,r) r^22 = +1/12*R(0,0,r) +11/52*R(2,0,r) +275/1092*R(4,0,r) +11/52*R(6,0,r) +99/728*R(8,0,r) +121/1768*R(10,0,r) +11/408*R(12,0,r) +275/33592*R(14,0,r) +11/5928*R(16,0,r) +11/37128*R(18,0,r) +1/33592*R(20,0,r) +1/705432*R(22,0,r) m = 1 r^1 = +1*R(1,1,r) r^3 = +2/3*R(1,1,r) +1/3*R(3,1,r) r^5 = +1/2*R(1,1,r) +2/5*R(3,1,r) +1/10*R(5,1,r) r^7 = +2/5*R(1,1,r) +2/5*R(3,1,r) +6/35*R(5,1,r) +1/35*R(7,1,r) r^9 = +1/3*R(1,1,r) +8/21*R(3,1,r) +3/14*R(5,1,r) +4/63*R(7,1,r) +1/126*R(9,1,r) r^11 = +2/7*R(1,1,r) +5/14*R(3,1,r) +5/21*R(5,1,r) +2/21*R(7,1,r) +5/231*R(9,1,r) +1/462*R(11,1,r) r^13 = +1/4*R(1,1,r) +1/3*R(3,1,r) +1/4*R(5,1,r) +4/33*R(7,1,r) +5/132*R(9,1,r) +1/143*R(11,1,r) +1/1716*R(13,1,r) r^15 = +2/9*R(1,1,r) +14/45*R(3,1,r) +14/55*R(5,1,r) +14/99*R(7,1,r) +70/1287*R(9,1,r) +2/143*R(11,1,r) +14/6435*R(13,1,r) +1/6435*R(15,1,r) r^17 = +1/5*R(1,1,r) +16/55*R(3,1,r) +14/55*R(5,1,r) +112/715*R(7,1,r) +10/143*R(9,1,r) +16/715*R(11,1,r) +7/1430*R(13,1,r) +8/12155*R(15,1,r) +1/24310*R(17,1,r) r^19 = +2/11*R(1,1,r) +3/11*R(3,1,r) +36/143*R(5,1,r) +24/143*R(7,1,r) +12/143*R(9,1,r) +9/286*R(11,1,r) +21/2431*R(13,1,r) +4/2431*R(15,1,r) +9/46189*R(17,1,r) +1/92378*R(19,1,r) r^21 = +1/6*R(1,1,r) +10/39*R(3,1,r) +45/182*R(5,1,r) +16/91*R(7,1,r) +5/52*R(9,1,r) +9/221*R(11,1,r) +35/2652*R(13,1,r) +40/12597*R(15,1,r) +9/16796*R(17,1,r) +5/88179*R(19,1,r) +1/352716*R(21,1,r) r^23 = +2/13*R(1,1,r) +22/91*R(3,1,r) +22/91*R(5,1,r) +33/182*R(7,1,r) +165/1547*R(9,1,r) +11/221*R(11,1,r) +77/4199*R(13,1,r) +22/4199*R(15,1,r) +33/29393*R(17,1,r) +5/29393*R(19,1,r) +11/676039*R(21,1,r) +1/1352078*R(23,1,r) m = 2 r^2 = +1*R(2,2,r) r^4 = +3/4*R(2,2,r) +1/4*R(4,2,r) r^6 = +3/5*R(2,2,r) +1/3*R(4,2,r) +1/15*R(6,2,r) r^8 = +1/2*R(2,2,r) +5/14*R(4,2,r) +1/8*R(6,2,r) +1/56*R(8,2,r) r^10 = +3/7*R(2,2,r) +5/14*R(4,2,r) +1/6*R(6,2,r) +3/70*R(8,2,r) +1/210*R(10,2,r) r^12 = +3/8*R(2,2,r) +25/72*R(4,2,r) +7/36*R(6,2,r) +3/44*R(8,2,r) +1/72*R(10,2,r) +1/792*R(12,2,r) r^14 = +1/3*R(2,2,r) +1/3*R(4,2,r) +7/33*R(6,2,r) +1/11*R(8,2,r) +1/39*R(10,2,r) +1/231*R(12,2,r) +1/3003*R(14,2,r) r^16 = +3/10*R(2,2,r) +7/22*R(4,2,r) +49/220*R(6,2,r) +63/572*R(8,2,r) +1/26*R(10,2,r) +1/110*R(12,2,r) +3/2288*R(14,2,r) +1/11440*R(16,2,r) r^18 = +3/11*R(2,2,r) +10/33*R(4,2,r) +98/429*R(6,2,r) +18/143*R(8,2,r) +2/39*R(10,2,r) +1/66*R(12,2,r) +15/4862*R(14,2,r) +1/2574*R(16,2,r) +1/43758*R(18,2,r) r^20 = +1/4*R(2,2,r) +15/52*R(4,2,r) +3/13*R(6,2,r) +9/65*R(8,2,r) +33/520*R(10,2,r) +3/136*R(12,2,r) +5/884*R(14,2,r) +1/988*R(16,2,r) +1/8840*R(18,2,r) +1/167960*R(20,2,r) r^22 = +3/13*R(2,2,r) +25/91*R(4,2,r) +3/13*R(6,2,r) +27/182*R(8,2,r) +33/442*R(10,2,r) +1/34*R(12,2,r) +75/8398*R(14,2,r) +1/494*R(16,2,r) +1/3094*R(18,2,r) +3/92378*R(20,2,r) +1/646646*R(22,2,r) r^24 = +3/14*R(2,2,r) +11/42*R(4,2,r) +11/48*R(6,2,r) +297/1904*R(8,2,r) +121/1428*R(10,2,r) +143/3876*R(12,2,r) +33/2584*R(14,2,r) +11/3192*R(16,2,r) +1/1428*R(18,2,r) +3/29716*R(20,2,r) +1/108528*R(22,2,r) +1/2496144*R(24,2,r) m = 3 r^3 = +1*R(3,3,r) r^5 = +4/5*R(3,3,r) +1/5*R(5,3,r) r^7 = +2/3*R(3,3,r) +2/7*R(5,3,r) +1/21*R(7,3,r) r^9 = +4/7*R(3,3,r) +9/28*R(5,3,r) +2/21*R(7,3,r) +1/84*R(9,3,r) r^11 = +1/2*R(3,3,r) +1/3*R(5,3,r) +2/15*R(7,3,r) +1/33*R(9,3,r) +1/330*R(11,3,r) r^13 = +4/9*R(3,3,r) +1/3*R(5,3,r) +16/99*R(7,3,r) +5/99*R(9,3,r) +4/429*R(11,3,r) +1/1287*R(13,3,r) r^15 = +2/5*R(3,3,r) +18/55*R(5,3,r) +2/11*R(7,3,r) +10/143*R(9,3,r) +18/1001*R(11,3,r) +2/715*R(13,3,r) +1/5005*R(15,3,r) r^17 = +4/11*R(3,3,r) +7/22*R(5,3,r) +28/143*R(7,3,r) +25/286*R(9,3,r) +4/143*R(11,3,r) +7/1144*R(13,3,r) +2/2431*R(15,3,r) +1/19448*R(17,3,r) r^19 = +1/3*R(3,3,r) +4/13*R(5,3,r) +8/39*R(7,3,r) +4/39*R(9,3,r) +1/26*R(11,3,r) +7/663*R(13,3,r) +4/1989*R(15,3,r) +1/4199*R(17,3,r) +1/75582*R(19,3,r) r^21 = +4/13*R(3,3,r) +27/91*R(5,3,r) +96/455*R(7,3,r) +3/26*R(9,3,r) +54/1105*R(11,3,r) +7/442*R(13,3,r) +16/4199*R(15,3,r) +27/41990*R(17,3,r) +2/29393*R(19,3,r) +1/293930*R(21,3,r) r^23 = +2/7*R(3,3,r) +2/7*R(5,3,r) +3/14*R(7,3,r) +15/119*R(9,3,r) +1/17*R(11,3,r) +7/323*R(13,3,r) +2/323*R(15,3,r) +3/2261*R(17,3,r) +5/24871*R(19,3,r) +1/52003*R(21,3,r) +1/1144066*R(23,3,r) r^25 = +4/15*R(3,3,r) +11/40*R(5,3,r) +11/51*R(7,3,r) +55/408*R(9,3,r) +22/323*R(11,3,r) +539/19380*R(13,3,r) +44/4845*R(15,3,r) +3/1292*R(17,3,r) +10/22287*R(19,3,r) +11/178296*R(21,3,r) +1/185725*R(23,3,r) +1/4457400*R(25,3,r) m = 4 r^4 = +1*R(4,4,r) r^6 = +5/6*R(4,4,r) +1/6*R(6,4,r) r^8 = +5/7*R(4,4,r) +1/4*R(6,4,r) +1/28*R(8,4,r) r^10 = +5/8*R(4,4,r) +7/24*R(6,4,r) +3/40*R(8,4,r) +1/120*R(10,4,r) r^12 = +5/9*R(4,4,r) +14/45*R(6,4,r) +6/55*R(8,4,r) +1/45*R(10,4,r) +1/495*R(12,4,r) r^14 = +1/2*R(4,4,r) +7/22*R(6,4,r) +3/22*R(8,4,r) +1/26*R(10,4,r) +1/154*R(12,4,r) +1/2002*R(14,4,r) r^16 = +5/11*R(4,4,r) +7/22*R(6,4,r) +45/286*R(8,4,r) +5/91*R(10,4,r) +1/77*R(12,4,r) +15/8008*R(14,4,r) +1/8008*R(16,4,r) r^18 = +5/12*R(4,4,r) +49/156*R(6,4,r) +9/52*R(8,4,r) +11/156*R(10,4,r) +1/48*R(12,4,r) +15/3536*R(14,4,r) +1/1872*R(16,4,r) +1/31824*R(18,4,r) r^20 = +5/13*R(4,4,r) +4/13*R(6,4,r) +12/65*R(8,4,r) +11/130*R(10,4,r) +1/34*R(12,4,r) +5/663*R(14,4,r) +1/741*R(16,4,r) +1/6630*R(18,4,r) +1/125970*R(20,4,r) r^22 = +5/14*R(4,4,r) +3/10*R(6,4,r) +27/140*R(8,4,r) +33/340*R(10,4,r) +13/340*R(12,4,r) +15/1292*R(14,4,r) +1/380*R(16,4,r) +1/2380*R(18,4,r) +3/71060*R(20,4,r) +1/497420*R(22,4,r) r^24 = +1/3*R(4,4,r) +7/24*R(6,4,r) +27/136*R(8,4,r) +11/102*R(10,4,r) +91/1938*R(12,4,r) +21/1292*R(14,4,r) +1/228*R(16,4,r) +1/1122*R(18,4,r) +21/163438*R(20,4,r) +1/85272*R(22,4,r) +1/1961256*R(24,4,r) r^26 = +5/16*R(4,4,r) +77/272*R(6,4,r) +55/272*R(8,4,r) +605/5168*R(10,4,r) +143/2584*R(12,4,r) +55/2584*R(14,4,r) +1/152*R(16,4,r) +5/3128*R(18,4,r) +35/118864*R(20,4,r) +1/25840*R(22,4,r) +5/1545232*R(24,4,r) +1/7726160*R(26,4,r) m = 5 r^5 = +1*R(5,5,r) r^7 = +6/7*R(5,5,r) +1/7*R(7,5,r) r^9 = +3/4*R(5,5,r) +2/9*R(7,5,r) +1/36*R(9,5,r) r^11 = +2/3*R(5,5,r) +4/15*R(7,5,r) +2/33*R(9,5,r) +1/165*R(11,5,r) r^13 = +3/5*R(5,5,r) +16/55*R(7,5,r) +1/11*R(9,5,r) +12/715*R(11,5,r) +1/715*R(13,5,r) r^15 = +6/11*R(5,5,r) +10/33*R(7,5,r) +50/429*R(9,5,r) +30/1001*R(11,5,r) +2/429*R(13,5,r) +1/3003*R(15,5,r) r^17 = +1/2*R(5,5,r) +4/13*R(7,5,r) +25/182*R(9,5,r) +4/91*R(11,5,r) +1/104*R(13,5,r) +2/1547*R(15,5,r) +1/12376*R(17,5,r) r^19 = +6/13*R(5,5,r) +4/13*R(7,5,r) +2/13*R(9,5,r) +3/52*R(11,5,r) +7/442*R(13,5,r) +2/663*R(15,5,r) +3/8398*R(17,5,r) +1/50388*R(19,5,r) r^21 = +3/7*R(5,5,r) +32/105*R(7,5,r) +1/6*R(9,5,r) +6/85*R(11,5,r) +7/306*R(13,5,r) +16/2907*R(15,5,r) +3/3230*R(17,5,r) +2/20349*R(19,5,r) +1/203490*R(21,5,r) r^23 = +2/5*R(5,5,r) +3/10*R(7,5,r) +3/17*R(9,5,r) +7/85*R(11,5,r) +49/1615*R(13,5,r) +14/1615*R(15,5,r) +3/1615*R(17,5,r) +1/3553*R(19,5,r) +1/37145*R(21,5,r) +1/817190*R(23,5,r) r^25 = +3/8*R(5,5,r) +5/17*R(7,5,r) +25/136*R(9,5,r) +30/323*R(11,5,r) +49/1292*R(13,5,r) +4/323*R(15,5,r) +45/14212*R(17,5,r) +50/81719*R(19,5,r) +5/59432*R(21,5,r) +3/408595*R(23,5,r) +1/3268760*R(25,5,r) r^27 = +6/17*R(5,5,r) +44/153*R(7,5,r) +550/2907*R(9,5,r) +33/323*R(11,5,r) +44/969*R(13,5,r) +16/969*R(15,5,r) +36/7429*R(17,5,r) +25/22287*R(19,5,r) +22/111435*R(21,5,r) +12/482885*R(23,5,r) +2/1002915*R(25,5,r) +1/13037895*R(27,5,r) m = 6 r^6 = +1*R(6,6,r) r^8 = +7/8*R(6,6,r) +1/8*R(8,6,r) r^10 = +7/9*R(6,6,r) +1/5*R(8,6,r) +1/45*R(10,6,r) r^12 = +7/10*R(6,6,r) +27/110*R(8,6,r) +1/20*R(10,6,r) +1/220*R(12,6,r) r^14 = +7/11*R(6,6,r) +3/11*R(8,6,r) +1/13*R(10,6,r) +1/77*R(12,6,r) +1/1001*R(14,6,r) r^16 = +7/12*R(6,6,r) +15/52*R(8,6,r) +55/546*R(10,6,r) +1/42*R(12,6,r) +5/1456*R(14,6,r) +1/4368*R(16,6,r) r^18 = +7/13*R(6,6,r) +27/91*R(8,6,r) +11/91*R(10,6,r) +1/28*R(12,6,r) +45/6188*R(14,6,r) +1/1092*R(16,6,r) +1/18564*R(18,6,r) r^20 = +1/2*R(6,6,r) +3/10*R(8,6,r) +11/80*R(10,6,r) +13/272*R(12,6,r) +5/408*R(14,6,r) +1/456*R(16,6,r) +1/4080*R(18,6,r) +1/77520*R(20,6,r) r^22 = +7/15*R(6,6,r) +3/10*R(8,6,r) +77/510*R(10,6,r) +91/1530*R(12,6,r) +35/1938*R(14,6,r) +7/1710*R(16,6,r) +1/1530*R(18,6,r) +7/106590*R(20,6,r) +1/319770*R(22,6,r) r^24 = +7/16*R(6,6,r) +81/272*R(8,6,r) +11/68*R(10,6,r) +91/1292*R(12,6,r) +63/2584*R(14,6,r) +1/152*R(16,6,r) +1/748*R(18,6,r) +63/326876*R(20,6,r) +1/56848*R(22,6,r) +1/1307504*R(24,6,r) r^26 = +7/17*R(6,6,r) +5/17*R(8,6,r) +55/323*R(10,6,r) +26/323*R(12,6,r) +10/323*R(14,6,r) +2/209*R(16,6,r) +10/4301*R(18,6,r) +35/81719*R(20,6,r) +1/17765*R(22,6,r) +5/1062347*R(24,6,r) +1/5311735*R(26,6,r) r^28 = +7/18*R(6,6,r) +11/38*R(8,6,r) +121/684*R(10,6,r) +143/1596*R(12,6,r) +5/133*R(14,6,r) +17/1311*R(16,6,r) +1/276*R(18,6,r) +7/8740*R(20,6,r) +1/7410*R(22,6,r) +5/306774*R(24,6,r) +1/795340*R(26,6,r) +1/21474180*R(28,6,r) m = 7 r^7 = +1*R(7,7,r) r^9 = +8/9*R(7,7,r) +1/9*R(9,7,r) r^11 = +4/5*R(7,7,r) +2/11*R(9,7,r) +1/55*R(11,7,r) r^13 = +8/11*R(7,7,r) +5/22*R(9,7,r) +6/143*R(11,7,r) +1/286*R(13,7,r) r^15 = +2/3*R(7,7,r) +10/39*R(9,7,r) +6/91*R(11,7,r) +2/195*R(13,7,r) +1/1365*R(15,7,r) r^17 = +8/13*R(7,7,r) +25/91*R(9,7,r) +8/91*R(11,7,r) +1/52*R(13,7,r) +4/1547*R(15,7,r) +1/6188*R(17,7,r) r^19 = +4/7*R(7,7,r) +2/7*R(9,7,r) +3/28*R(11,7,r) +1/34*R(13,7,r) +2/357*R(15,7,r) +3/4522*R(17,7,r) +1/27132*R(19,7,r) r^21 = +8/15*R(7,7,r) +7/24*R(9,7,r) +21/170*R(11,7,r) +49/1224*R(13,7,r) +28/2907*R(15,7,r) +21/12920*R(17,7,r) +1/5814*R(19,7,r) +1/116280*R(21,7,r) r^23 = +1/2*R(7,7,r) +5/17*R(9,7,r) +7/51*R(11,7,r) +49/969*R(13,7,r) +14/969*R(15,7,r) +1/323*R(17,7,r) +5/10659*R(19,7,r) +1/22287*R(21,7,r) +1/490314*R(23,7,r) r^25 = +8/17*R(7,7,r) +5/17*R(9,7,r) +48/323*R(11,7,r) +98/1615*R(13,7,r) +32/1615*R(15,7,r) +18/3553*R(17,7,r) +80/81719*R(19,7,r) +1/7429*R(21,7,r) +24/2042975*R(23,7,r) +1/2042975*R(25,7,r) r^27 = +4/9*R(7,7,r) +50/171*R(9,7,r) +3/19*R(11,7,r) +4/57*R(13,7,r) +16/627*R(15,7,r) +36/4807*R(17,7,r) +25/14421*R(19,7,r) +2/6555*R(21,7,r) +12/312455*R(23,7,r) +2/648945*R(25,7,r) +1/8436285*R(27,7,r) r^29 = +8/19*R(7,7,r) +11/38*R(9,7,r) +22/133*R(11,7,r) +3/38*R(13,7,r) +96/3059*R(15,7,r) +9/874*R(17,7,r) +6/2185*R(19,7,r) +33/56810*R(21,7,r) +8/85215*R(23,7,r) +1/91770*R(25,7,r) +2/2471235*R(27,7,r) +1/34597290*R(29,7,r) m = 8 r^8 = +1*R(8,8,r) r^10 = +9/10*R(8,8,r) +1/10*R(10,8,r) r^12 = +9/11*R(8,8,r) +1/6*R(10,8,r) +1/66*R(12,8,r) r^14 = +3/4*R(8,8,r) +11/52*R(10,8,r) +1/28*R(12,8,r) +1/364*R(14,8,r) r^16 = +9/13*R(8,8,r) +22/91*R(10,8,r) +2/35*R(12,8,r) +3/364*R(14,8,r) +1/1820*R(16,8,r) r^18 = +9/14*R(8,8,r) +11/42*R(10,8,r) +13/168*R(12,8,r) +15/952*R(14,8,r) +1/504*R(16,8,r) +1/8568*R(18,8,r) r^20 = +3/5*R(8,8,r) +11/40*R(10,8,r) +13/136*R(12,8,r) +5/204*R(14,8,r) +1/228*R(16,8,r) +1/2040*R(18,8,r) +1/38760*R(20,8,r) r^22 = +9/16*R(8,8,r) +77/272*R(10,8,r) +91/816*R(12,8,r) +175/5168*R(14,8,r) +7/912*R(16,8,r) +1/816*R(18,8,r) +7/56848*R(20,8,r) +1/170544*R(22,8,r) r^24 = +9/17*R(8,8,r) +44/153*R(10,8,r) +364/2907*R(12,8,r) +14/323*R(14,8,r) +2/171*R(16,8,r) +4/1683*R(18,8,r) +28/81719*R(20,8,r) +1/31977*R(22,8,r) +1/735471*R(24,8,r) r^26 = +1/2*R(8,8,r) +11/38*R(10,8,r) +13/95*R(12,8,r) +1/19*R(14,8,r) +17/1045*R(16,8,r) +1/253*R(18,8,r) +7/9614*R(20,8,r) +1/10450*R(22,8,r) +1/124982*R(24,8,r) +1/3124550*R(26,8,r) r^28 = +9/19*R(8,8,r) +11/38*R(10,8,r) +39/266*R(12,8,r) +90/1463*R(14,8,r) +102/4807*R(16,8,r) +3/506*R(18,8,r) +63/48070*R(20,8,r) +3/13585*R(22,8,r) +5/187473*R(24,8,r) +9/4374370*R(26,8,r) +1/13123110*R(28,8,r) r^30 = +9/20*R(8,8,r) +121/420*R(10,8,r) +13/84*R(12,8,r) +45/644*R(14,8,r) +17/644*R(16,8,r) +19/2300*R(18,8,r) +63/29900*R(20,8,r) +1/2340*R(22,8,r) +5/75348*R(24,8,r) +9/1213940*R(26,8,r) +1/1883700*R(28,8,r) +1/54627300*R(30,8,r) m = 9 r^9 = +1*R(9,9,r) r^11 = +10/11*R(9,9,r) +1/11*R(11,9,r) r^13 = +5/6*R(9,9,r) +2/13*R(11,9,r) +1/78*R(13,9,r) r^15 = +10/13*R(9,9,r) +18/91*R(11,9,r) +2/65*R(13,9,r) +1/455*R(15,9,r) r^17 = +5/7*R(9,9,r) +8/35*R(11,9,r) +1/20*R(13,9,r) +4/595*R(15,9,r) +1/2380*R(17,9,r) r^19 = +2/3*R(9,9,r) +1/4*R(11,9,r) +7/102*R(13,9,r) +2/153*R(15,9,r) +1/646*R(17,9,r) +1/11628*R(19,9,r) r^21 = +5/8*R(9,9,r) +9/34*R(11,9,r) +35/408*R(13,9,r) +20/969*R(15,9,r) +9/2584*R(17,9,r) +5/13566*R(19,9,r) +1/54264*R(21,9,r) r^23 = +10/17*R(9,9,r) +14/51*R(11,9,r) +98/969*R(13,9,r) +28/969*R(15,9,r) +2/323*R(17,9,r) +10/10659*R(19,9,r) +2/22287*R(21,9,r) +1/245157*R(23,9,r) r^25 = +5/9*R(9,9,r) +16/57*R(11,9,r) +98/855*R(13,9,r) +32/855*R(15,9,r) +2/209*R(17,9,r) +80/43263*R(19,9,r) +1/3933*R(21,9,r) +8/360525*R(23,9,r) +1/1081575*R(25,9,r) r^27 = +10/19*R(9,9,r) +27/95*R(11,9,r) +12/95*R(13,9,r) +48/1045*R(15,9,r) +324/24035*R(17,9,r) +15/4807*R(19,9,r) +6/10925*R(21,9,r) +108/1562275*R(23,9,r) +2/360525*R(25,9,r) +1/4686825*R(27,9,r) r^29 = +1/2*R(9,9,r) +2/7*R(11,9,r) +3/22*R(13,9,r) +96/1771*R(15,9,r) +9/506*R(17,9,r) +6/1265*R(19,9,r) +3/2990*R(21,9,r) +8/49335*R(23,9,r) +1/53130*R(25,9,r) +2/1430715*R(27,9,r) +1/20030010*R(29,9,r) r^31 = +10/21*R(9,9,r) +2/7*R(11,9,r) +10/69*R(13,9,r) +10/161*R(15,9,r) +18/805*R(17,9,r) +2/299*R(19,9,r) +22/13455*R(21,9,r) +2/6279*R(23,9,r) +2/42021*R(25,9,r) +2/390195*R(27,9,r) +2/5644821*R(29,9,r) +1/84672315*R(31,9,r) m = 10 r^10 = +1*R(10,10,r) r^12 = +11/12*R(10,10,r) +1/12*R(12,10,r) r^14 = +11/13*R(10,10,r) +1/7*R(12,10,r) +1/91*R(14,10,r) r^16 = +11/14*R(10,10,r) +13/70*R(12,10,r) +3/112*R(14,10,r) +1/560*R(16,10,r) r^18 = +11/15*R(10,10,r) +13/60*R(12,10,r) +3/68*R(14,10,r) +1/180*R(16,10,r) +1/3060*R(18,10,r) r^20 = +11/16*R(10,10,r) +65/272*R(12,10,r) +25/408*R(14,10,r) +5/456*R(16,10,r) +1/816*R(18,10,r) +1/15504*R(20,10,r) r^22 = +11/17*R(10,10,r) +13/51*R(12,10,r) +25/323*R(14,10,r) +1/57*R(16,10,r) +1/357*R(18,10,r) +1/3553*R(20,10,r) +1/74613*R(22,10,r) r^24 = +11/18*R(10,10,r) +91/342*R(12,10,r) +7/76*R(14,10,r) +17/684*R(16,10,r) +1/198*R(18,10,r) +7/9614*R(20,10,r) +1/15048*R(22,10,r) +1/346104*R(24,10,r) r^26 = +11/19*R(10,10,r) +26/95*R(12,10,r) +2/19*R(14,10,r) +34/1045*R(16,10,r) +2/253*R(18,10,r) +7/4807*R(20,10,r) +1/5225*R(22,10,r) +1/62491*R(24,10,r) +1/1562275*R(26,10,r) r^28 = +11/20*R(10,10,r) +39/140*R(12,10,r) +9/77*R(14,10,r) +51/1265*R(16,10,r) +57/5060*R(18,10,r) +63/25300*R(20,10,r) +3/7150*R(22,10,r) +1/19734*R(24,10,r) +9/2302300*R(26,10,r) +1/6906900*R(28,10,r) r^30 = +11/21*R(10,10,r) +65/231*R(12,10,r) +225/1771*R(14,10,r) +85/1771*R(16,10,r) +19/1265*R(18,10,r) +63/16445*R(20,10,r) +1/1287*R(22,10,r) +25/207207*R(24,10,r) +9/667667*R(26,10,r) +1/1036035*R(28,10,r) +1/30045015*R(30,10,r) r^32 = +1/2*R(10,10,r) +13/46*R(12,10,r) +25/184*R(14,10,r) +51/920*R(16,10,r) +57/2990*R(18,10,r) +49/8970*R(20,10,r) +1/780*R(22,10,r) +25/104052*R(24,10,r) +3/86710*R(26,10,r) +1/278070*R(28,10,r) +1/4162080*R(30,10,r) +1/129024480*R(32,10,r) Bivariate Cartesian to Zernike Polynomials, X=r*cos(phi), Y=r*sin(phi): X = R(1,1,r)*cos(phi) Y = R(1,1,r)*sin(phi) X^2 = 1/2*R(2,2,r)*cos(2*phi) +1/4*R(0,0,r) +1/4*R(2,0,r) X*Y = 1/2*R(2,2,r)*sin(2*phi) Y^2 = -1/2*R(2,2,r)*cos(2*phi) +1/4*R(0,0,r) +1/4*R(2,0,r) X^3 = 1/4*R(3,3,r)*cos(3*phi) +1/2*cos(phi)*R(1,1,r) +1/4*cos(phi)*R(3,1,r) X^2*Y = 1/4*R(3,3,r)*sin(3*phi) +1/6*sin(phi)*R(1,1,r) +1/12*sin(phi)*R(3,1,r) X*Y^2 = -1/4*R(3,3,r)*cos(3*phi) +1/6*cos(phi)*R(1,1,r) +1/12*cos(phi)*R(3,1,r) Y^3 = -1/4*R(3,3,r)*sin(3*phi) +1/2*sin(phi)*R(1,1,r) +1/4*sin(phi)*R(3,1,r) X^4 = 1/8*R(4,4,r)*cos(4*phi) +3/8*cos(2*phi)*R(2,2,r) +1/8*cos(2*phi)*R(4,2,r) +1/8*R(0,0,r) +3/16*R(2,0,r) +1/16*R(4,0,r) X^3*Y = 1/8*R(4,4,r)*sin(4*phi) +3/16*sin(2*phi)*R(2,2,r) +1/16*sin(2*phi)*R(4,2,r) X^2*Y^2 = -1/8*R(4,4,r)*cos(4*phi) +1/24*R(0,0,r) +1/16*R(2,0,r) +1/48*R(4,0,r) X*Y^3 = -1/8*R(4,4,r)*sin(4*phi) +3/16*sin(2*phi)*R(2,2,r) +1/16*sin(2*phi)*R(4,2,r) Y^4 = 1/8*R(4,4,r)*cos(4*phi) -3/8*cos(2*phi)*R(2,2,r) -1/8*cos(2*phi)*R(4,2,r) +1/8*R(0,0,r) +3/16*R(2,0,r) +1/16*R(4,0,r) X^5 = 1/16*R(5,5,r)*cos(5*phi) +1/4*cos(3*phi)*R(3,3,r) +1/16*cos(3*phi)*R(5,3,r) +5/16*cos(phi)*R(1,1,r) +1/4*cos(phi)*R(3,1,r) +1/16*cos(phi)*R(5,1,r) X^4*Y = 1/16*R(5,5,r)*sin(5*phi) +3/20*sin(3*phi)*R(3,3,r) +3/80*sin(3*phi)*R(5,3,r) +1/16*sin(phi)*R(1,1,r) +1/20*sin(phi)*R(3,1,r) +1/80*sin(phi)*R(5,1,r) X^3*Y^2 = -1/16*R(5,5,r)*cos(5*phi) -1/20*cos(3*phi)*R(3,3,r) -1/80*cos(3*phi)*R(5,3,r) +1/16*cos(phi)*R(1,1,r) +1/20*cos(phi)*R(3,1,r) +1/80*cos(phi)*R(5,1,r) X^2*Y^3 = -1/16*R(5,5,r)*sin(5*phi) +1/20*sin(3*phi)*R(3,3,r) +1/80*sin(3*phi)*R(5,3,r) +1/16*sin(phi)*R(1,1,r) +1/20*sin(phi)*R(3,1,r) +1/80*sin(phi)*R(5,1,r) X*Y^4 = 1/16*R(5,5,r)*cos(5*phi) -3/20*cos(3*phi)*R(3,3,r) -3/80*cos(3*phi)*R(5,3,r) +1/16*cos(phi)*R(1,1,r) +1/20*cos(phi)*R(3,1,r) +1/80*cos(phi)*R(5,1,r) Y^5 = 1/16*R(5,5,r)*sin(5*phi) -1/4*sin(3*phi)*R(3,3,r) -1/16*sin(3*phi)*R(5,3,r) +5/16*sin(phi)*R(1,1,r) +1/4*sin(phi)*R(3,1,r) +1/16*sin(phi)*R(5,1,r) X^6 = 1/32*R(6,6,r)*cos(6*phi) +5/32*cos(4*phi)*R(4,4,r) +1/32*cos(4*phi)*R(6,4,r) +9/32*cos(2*phi)*R(2,2,r) +5/32*cos(2*phi)*R(4,2,r) +1/32*cos(2*phi)*R(6,2,r) +5/64*R(0,0,r) +9/64*R(2,0,r) +5/64*R(4,0,r) +1/64*R(6,0,r) X^5*Y = 1/32*R(6,6,r)*sin(6*phi) +5/48*sin(4*phi)*R(4,4,r) +1/48*sin(4*phi)*R(6,4,r) +3/32*sin(2*phi)*R(2,2,r) +5/96*sin(2*phi)*R(4,2,r) +1/96*sin(2*phi)*R(6,2,r) X^4*Y^2 = -1/32*R(6,6,r)*cos(6*phi) -5/96*cos(4*phi)*R(4,4,r) -1/96*cos(4*phi)*R(6,4,r) +3/160*cos(2*phi)*R(2,2,r) +1/96*cos(2*phi)*R(4,2,r) +1/480*cos(2*phi)*R(6,2,r) +1/64*R(0,0,r) +9/320*R(2,0,r) +1/64*R(4,0,r) +1/320*R(6,0,r) X^3*Y^3 = -1/32*R(6,6,r)*sin(6*phi) +9/160*sin(2*phi)*R(2,2,r) +1/32*sin(2*phi)*R(4,2,r) +1/160*sin(2*phi)*R(6,2,r) X^2*Y^4 = 1/32*R(6,6,r)*cos(6*phi) -5/96*cos(4*phi)*R(4,4,r) -1/96*cos(4*phi)*R(6,4,r) -3/160*cos(2*phi)*R(2,2,r) -1/96*cos(2*phi)*R(4,2,r) -1/480*cos(2*phi)*R(6,2,r) +1/64*R(0,0,r) +9/320*R(2,0,r) +1/64*R(4,0,r) +1/320*R(6,0,r) X*Y^5 = 1/32*R(6,6,r)*sin(6*phi) -5/48*sin(4*phi)*R(4,4,r) -1/48*sin(4*phi)*R(6,4,r) +3/32*sin(2*phi)*R(2,2,r) +5/96*sin(2*phi)*R(4,2,r) +1/96*sin(2*phi)*R(6,2,r) Y^6 = -1/32*R(6,6,r)*cos(6*phi) +5/32*cos(4*phi)*R(4,4,r) +1/32*cos(4*phi)*R(6,4,r) -9/32*cos(2*phi)*R(2,2,r) -5/32*cos(2*phi)*R(4,2,r) -1/32*cos(2*phi)*R(6,2,r) +5/64*R(0,0,r) +9/64*R(2,0,r) +5/64*R(4,0,r) +1/64*R(6,0,r) X^7 = 1/64*R(7,7,r)*cos(7*phi) +3/32*cos(5*phi)*R(5,5,r) +1/64*cos(5*phi)*R(7,5,r) +7/32*cos(3*phi)*R(3,3,r) +3/32*cos(3*phi)*R(5,3,r) +1/64*cos(3*phi)*R(7,3,r) +7/32*cos(phi)*R(1,1,r) +7/32*cos(phi)*R(3,1,r) +3/32*cos(phi)*R(5,1,r) +1/64*cos(phi)*R(7,1,r) X^6*Y = 1/64*R(7,7,r)*sin(7*phi) +15/224*sin(5*phi)*R(5,5,r) +5/448*sin(5*phi)*R(7,5,r) +3/32*sin(3*phi)*R(3,3,r) +9/224*sin(3*phi)*R(5,3,r) +3/448*sin(3*phi)*R(7,3,r) +1/32*sin(phi)*R(1,1,r) +1/32*sin(phi)*R(3,1,r) +3/224*sin(phi)*R(5,1,r) +1/448*sin(phi)*R(7,1,r) X^5*Y^2 = -1/64*R(7,7,r)*cos(7*phi) -9/224*cos(5*phi)*R(5,5,r) -3/448*cos(5*phi)*R(7,5,r) -1/96*cos(3*phi)*R(3,3,r) -1/224*cos(3*phi)*R(5,3,r) -1/1344*cos(3*phi)*R(7,3,r) +1/32*cos(phi)*R(1,1,r) +1/32*cos(phi)*R(3,1,r) +3/224*cos(phi)*R(5,1,r) +1/448*cos(phi)*R(7,1,r) X^4*Y^3 = -1/64*R(7,7,r)*sin(7*phi) -3/224*sin(5*phi)*R(5,5,r) -1/448*sin(5*phi)*R(7,5,r) +1/32*sin(3*phi)*R(3,3,r) +3/224*sin(3*phi)*R(5,3,r) +1/448*sin(3*phi)*R(7,3,r) +3/160*sin(phi)*R(1,1,r) +3/160*sin(phi)*R(3,1,r) +9/1120*sin(phi)*R(5,1,r) +3/2240*sin(phi)*R(7,1,r) X^3*Y^4 = 1/64*R(7,7,r)*cos(7*phi) -3/224*cos(5*phi)*R(5,5,r) -1/448*cos(5*phi)*R(7,5,r) -1/32*cos(3*phi)*R(3,3,r) -3/224*cos(3*phi)*R(5,3,r) -1/448*cos(3*phi)*R(7,3,r) +3/160*cos(phi)*R(1,1,r) +3/160*cos(phi)*R(3,1,r) +9/1120*cos(phi)*R(5,1,r) +3/2240*cos(phi)*R(7,1,r) X^2*Y^5 = 1/64*R(7,7,r)*sin(7*phi) -9/224*sin(5*phi)*R(5,5,r) -3/448*sin(5*phi)*R(7,5,r) +1/96*sin(3*phi)*R(3,3,r) +1/224*sin(3*phi)*R(5,3,r) +1/1344*sin(3*phi)*R(7,3,r) +1/32*sin(phi)*R(1,1,r) +1/32*sin(phi)*R(3,1,r) +3/224*sin(phi)*R(5,1,r) +1/448*sin(phi)*R(7,1,r) X*Y^6 = -1/64*R(7,7,r)*cos(7*phi) +15/224*cos(5*phi)*R(5,5,r) +5/448*cos(5*phi)*R(7,5,r) -3/32*cos(3*phi)*R(3,3,r) -9/224*cos(3*phi)*R(5,3,r) -3/448*cos(3*phi)*R(7,3,r) +1/32*cos(phi)*R(1,1,r) +1/32*cos(phi)*R(3,1,r) +3/224*cos(phi)*R(5,1,r) +1/448*cos(phi)*R(7,1,r) Y^7 = -1/64*R(7,7,r)*sin(7*phi) +3/32*sin(5*phi)*R(5,5,r) +1/64*sin(5*phi)*R(7,5,r) -7/32*sin(3*phi)*R(3,3,r) -3/32*sin(3*phi)*R(5,3,r) -1/64*sin(3*phi)*R(7,3,r) +7/32*sin(phi)*R(1,1,r) +7/32*sin(phi)*R(3,1,r) +3/32*sin(phi)*R(5,1,r) +1/64*sin(phi)*R(7,1,r) X^8 = 1/128*R(8,8,r)*cos(8*phi) +7/128*cos(6*phi)*R(6,6,r) +1/128*cos(6*phi)*R(8,6,r) +5/32*cos(4*phi)*R(4,4,r) +7/128*cos(4*phi)*R(6,4,r) +1/128*cos(4*phi)*R(8,4,r) +7/32*cos(2*phi)*R(2,2,r) +5/32*cos(2*phi)*R(4,2,r) +7/128*cos(2*phi)*R(6,2,r) +1/128*cos(2*phi)*R(8,2,r) +7/128*R(0,0,r) +7/64*R(2,0,r) +5/64*R(4,0,r) +7/256*R(6,0,r) +1/256*R(8,0,r) X^7*Y = 1/128*R(8,8,r)*sin(8*phi) +21/512*sin(6*phi)*R(6,6,r) +3/512*sin(6*phi)*R(8,6,r) +5/64*sin(4*phi)*R(4,4,r) +7/256*sin(4*phi)*R(6,4,r) +1/256*sin(4*phi)*R(8,4,r) +7/128*sin(2*phi)*R(2,2,r) +5/128*sin(2*phi)*R(4,2,r) +7/512*sin(2*phi)*R(6,2,r) +1/512*sin(2*phi)*R(8,2,r) X^6*Y^2 = -1/128*R(8,8,r)*cos(8*phi) -7/256*cos(6*phi)*R(6,6,r) -1/256*cos(6*phi)*R(8,6,r) -5/224*cos(4*phi)*R(4,4,r) -1/128*cos(4*phi)*R(6,4,r) -1/896*cos(4*phi)*R(8,4,r) +1/64*cos(2*phi)*R(2,2,r) +5/448*cos(2*phi)*R(4,2,r) +1/256*cos(2*phi)*R(6,2,r) +1/1792*cos(2*phi)*R(8,2,r) +1/128*R(0,0,r) +1/64*R(2,0,r) +5/448*R(4,0,r) +1/256*R(6,0,r) +1/1792*R(8,0,r) X^5*Y^3 = -1/128*R(8,8,r)*sin(8*phi) -7/512*sin(6*phi)*R(6,6,r) -1/512*sin(6*phi)*R(8,6,r) +5/448*sin(4*phi)*R(4,4,r) +1/256*sin(4*phi)*R(6,4,r) +1/1792*sin(4*phi)*R(8,4,r) +3/128*sin(2*phi)*R(2,2,r) +15/896*sin(2*phi)*R(4,2,r) +3/512*sin(2*phi)*R(6,2,r) +3/3584*sin(2*phi)*R(8,2,r) X^4*Y^4 = 1/128*R(8,8,r)*cos(8*phi) -5/224*cos(4*phi)*R(4,4,r) -1/128*cos(4*phi)*R(6,4,r) -1/896*cos(4*phi)*R(8,4,r) +3/640*R(0,0,r) +3/320*R(2,0,r) +3/448*R(4,0,r) +3/1280*R(6,0,r) +3/8960*R(8,0,r) X^3*Y^5 = 1/128*R(8,8,r)*sin(8*phi) -7/512*sin(6*phi)*R(6,6,r) -1/512*sin(6*phi)*R(8,6,r) -5/448*sin(4*phi)*R(4,4,r) -1/256*sin(4*phi)*R(6,4,r) -1/1792*sin(4*phi)*R(8,4,r) +3/128*sin(2*phi)*R(2,2,r) +15/896*sin(2*phi)*R(4,2,r) +3/512*sin(2*phi)*R(6,2,r) +3/3584*sin(2*phi)*R(8,2,r) X^2*Y^6 = -1/128*R(8,8,r)*cos(8*phi) +7/256*cos(6*phi)*R(6,6,r) +1/256*cos(6*phi)*R(8,6,r) -5/224*cos(4*phi)*R(4,4,r) -1/128*cos(4*phi)*R(6,4,r) -1/896*cos(4*phi)*R(8,4,r) -1/64*cos(2*phi)*R(2,2,r) -5/448*cos(2*phi)*R(4,2,r) -1/256*cos(2*phi)*R(6,2,r) -1/1792*cos(2*phi)*R(8,2,r) +1/128*R(0,0,r) +1/64*R(2,0,r) +5/448*R(4,0,r) +1/256*R(6,0,r) +1/1792*R(8,0,r) X*Y^7 = -1/128*R(8,8,r)*sin(8*phi) +21/512*sin(6*phi)*R(6,6,r) +3/512*sin(6*phi)*R(8,6,r) -5/64*sin(4*phi)*R(4,4,r) -7/256*sin(4*phi)*R(6,4,r) -1/256*sin(4*phi)*R(8,4,r) +7/128*sin(2*phi)*R(2,2,r) +5/128*sin(2*phi)*R(4,2,r) +7/512*sin(2*phi)*R(6,2,r) +1/512*sin(2*phi)*R(8,2,r) Y^8 = 1/128*R(8,8,r)*cos(8*phi) -7/128*cos(6*phi)*R(6,6,r) -1/128*cos(6*phi)*R(8,6,r) +5/32*cos(4*phi)*R(4,4,r) +7/128*cos(4*phi)*R(6,4,r) +1/128*cos(4*phi)*R(8,4,r) -7/32*cos(2*phi)*R(2,2,r) -5/32*cos(2*phi)*R(4,2,r) -7/128*cos(2*phi)*R(6,2,r) -1/128*cos(2*phi)*R(8,2,r) +7/128*R(0,0,r) +7/64*R(2,0,r) +5/64*R(4,0,r) +7/256*R(6,0,r) +1/256*R(8,0,r) X^9 = 1/256*R(9,9,r)*cos(9*phi) +1/32*cos(7*phi)*R(7,7,r) +1/256*cos(7*phi)*R(9,7,r) +27/256*cos(5*phi)*R(5,5,r) +1/32*cos(5*phi)*R(7,5,r) +1/256*cos(5*phi)*R(9,5,r) +3/16*cos(3*phi)*R(3,3,r) +27/256*cos(3*phi)*R(5,3,r) +1/32*cos(3*phi)*R(7,3,r) +1/256*cos(3*phi)*R(9,3,r) +21/128*cos(phi)*R(1,1,r) +3/16*cos(phi)*R(3,1,r) +27/256*cos(phi)*R(5,1,r) +1/32*cos(phi)*R(7,1,r) +1/256*cos(phi)*R(9,1,r) X^8*Y = 1/256*R(9,9,r)*sin(9*phi) +7/288*sin(7*phi)*R(7,7,r) +7/2304*sin(7*phi)*R(9,7,r) +15/256*sin(5*phi)*R(5,5,r) +5/288*sin(5*phi)*R(7,5,r) +5/2304*sin(5*phi)*R(9,5,r) +1/16*sin(3*phi)*R(3,3,r) +9/256*sin(3*phi)*R(5,3,r) +1/96*sin(3*phi)*R(7,3,r) +1/768*sin(3*phi)*R(9,3,r) +7/384*sin(phi)*R(1,1,r) +1/48*sin(phi)*R(3,1,r) +3/256*sin(phi)*R(5,1,r) +1/288*sin(phi)*R(7,1,r) +1/2304*sin(phi)*R(9,1,r) X^7*Y^2 = -1/256*R(9,9,r)*cos(9*phi) -5/288*cos(7*phi)*R(7,7,r) -5/2304*cos(7*phi)*R(9,7,r) -3/128*cos(5*phi)*R(5,5,r) -1/144*cos(5*phi)*R(7,5,r) -1/1152*cos(5*phi)*R(9,5,r) +7/384*cos(phi)*R(1,1,r) +1/48*cos(phi)*R(3,1,r) +3/256*cos(phi)*R(5,1,r) +1/288*cos(phi)*R(7,1,r) +1/2304*cos(phi)*R(9,1,r) X^6*Y^3 = -1/256*R(9,9,r)*sin(9*phi) -1/96*sin(7*phi)*R(7,7,r) -1/768*sin(7*phi)*R(9,7,r) +1/56*sin(3*phi)*R(3,3,r) +9/896*sin(3*phi)*R(5,3,r) +1/336*sin(3*phi)*R(7,3,r) +1/2688*sin(3*phi)*R(9,3,r) +1/128*sin(phi)*R(1,1,r) +1/112*sin(phi)*R(3,1,r) +9/1792*sin(phi)*R(5,1,r) +1/672*sin(phi)*R(7,1,r) +1/5376*sin(phi)*R(9,1,r) X^5*Y^4 = 1/256*R(9,9,r)*cos(9*phi) +1/288*cos(7*phi)*R(7,7,r) +1/2304*cos(7*phi)*R(9,7,r) -3/256*cos(5*phi)*R(5,5,r) -1/288*cos(5*phi)*R(7,5,r) -1/2304*cos(5*phi)*R(9,5,r) -1/112*cos(3*phi)*R(3,3,r) -9/1792*cos(3*phi)*R(5,3,r) -1/672*cos(3*phi)*R(7,3,r) -1/5376*cos(3*phi)*R(9,3,r) +1/128*cos(phi)*R(1,1,r) +1/112*cos(phi)*R(3,1,r) +9/1792*cos(phi)*R(5,1,r) +1/672*cos(phi)*R(7,1,r) +1/5376*cos(phi)*R(9,1,r) X^4*Y^5 = 1/256*R(9,9,r)*sin(9*phi) -1/288*sin(7*phi)*R(7,7,r) -1/2304*sin(7*phi)*R(9,7,r) -3/256*sin(5*phi)*R(5,5,r) -1/288*sin(5*phi)*R(7,5,r) -1/2304*sin(5*phi)*R(9,5,r) +1/112*sin(3*phi)*R(3,3,r) +9/1792*sin(3*phi)*R(5,3,r) +1/672*sin(3*phi)*R(7,3,r) +1/5376*sin(3*phi)*R(9,3,r) +1/128*sin(phi)*R(1,1,r) +1/112*sin(phi)*R(3,1,r) +9/1792*sin(phi)*R(5,1,r) +1/672*sin(phi)*R(7,1,r) +1/5376*sin(phi)*R(9,1,r) X^3*Y^6 = -1/256*R(9,9,r)*cos(9*phi) +1/96*cos(7*phi)*R(7,7,r) +1/768*cos(7*phi)*R(9,7,r) -1/56*cos(3*phi)*R(3,3,r) -9/896*cos(3*phi)*R(5,3,r) -1/336*cos(3*phi)*R(7,3,r) -1/2688*cos(3*phi)*R(9,3,r) +1/128*cos(phi)*R(1,1,r) +1/112*cos(phi)*R(3,1,r) +9/1792*cos(phi)*R(5,1,r) +1/672*cos(phi)*R(7,1,r) +1/5376*cos(phi)*R(9,1,r) X^2*Y^7 = -1/256*R(9,9,r)*sin(9*phi) +5/288*sin(7*phi)*R(7,7,r) +5/2304*sin(7*phi)*R(9,7,r) -3/128*sin(5*phi)*R(5,5,r) -1/144*sin(5*phi)*R(7,5,r) -1/1152*sin(5*phi)*R(9,5,r) +7/384*sin(phi)*R(1,1,r) +1/48*sin(phi)*R(3,1,r) +3/256*sin(phi)*R(5,1,r) +1/288*sin(phi)*R(7,1,r) +1/2304*sin(phi)*R(9,1,r) X*Y^8 = 1/256*R(9,9,r)*cos(9*phi) -7/288*cos(7*phi)*R(7,7,r) -7/2304*cos(7*phi)*R(9,7,r) +15/256*cos(5*phi)*R(5,5,r) +5/288*cos(5*phi)*R(7,5,r) +5/2304*cos(5*phi)*R(9,5,r) -1/16*cos(3*phi)*R(3,3,r) -9/256*cos(3*phi)*R(5,3,r) -1/96*cos(3*phi)*R(7,3,r) -1/768*cos(3*phi)*R(9,3,r) +7/384*cos(phi)*R(1,1,r) +1/48*cos(phi)*R(3,1,r) +3/256*cos(phi)*R(5,1,r) +1/288*cos(phi)*R(7,1,r) +1/2304*cos(phi)*R(9,1,r) Y^9 = 1/256*R(9,9,r)*sin(9*phi) -1/32*sin(7*phi)*R(7,7,r) -1/256*sin(7*phi)*R(9,7,r) +27/256*sin(5*phi)*R(5,5,r) +1/32*sin(5*phi)*R(7,5,r) +1/256*sin(5*phi)*R(9,5,r) -3/16*sin(3*phi)*R(3,3,r) -27/256*sin(3*phi)*R(5,3,r) -1/32*sin(3*phi)*R(7,3,r) -1/256*sin(3*phi)*R(9,3,r) +21/128*sin(phi)*R(1,1,r) +3/16*sin(phi)*R(3,1,r) +27/256*sin(phi)*R(5,1,r) +1/32*sin(phi)*R(7,1,r) +1/256*sin(phi)*R(9,1,r) X^10 = 1/512*R(10,10,r)*cos(10*phi) +9/512*cos(8*phi)*R(8,8,r) +1/512*cos(8*phi)*R(10,8,r) +35/512*cos(6*phi)*R(6,6,r) +9/512*cos(6*phi)*R(8,6,r) +1/512*cos(6*phi)*R(10,6,r) +75/512*cos(4*phi)*R(4,4,r) +35/512*cos(4*phi)*R(6,4,r) +9/512*cos(4*phi)*R(8,4,r) +1/512*cos(4*phi)*R(10,4,r) +45/256*cos(2*phi)*R(2,2,r) +75/512*cos(2*phi)*R(4,2,r) +35/512*cos(2*phi)*R(6,2,r) +9/512*cos(2*phi)*R(8,2,r) +1/512*cos(2*phi)*R(10,2,r) +21/512*R(0,0,r) +45/512*R(2,0,r) +75/1024*R(4,0,r) +35/1024*R(6,0,r) +9/1024*R(8,0,r) +1/1024*R(10,0,r) X^9*Y = 1/512*R(10,10,r)*sin(10*phi) +9/640*sin(8*phi)*R(8,8,r) +1/640*sin(8*phi)*R(10,8,r) +21/512*sin(6*phi)*R(6,6,r) +27/2560*sin(6*phi)*R(8,6,r) +3/2560*sin(6*phi)*R(10,6,r) +15/256*sin(4*phi)*R(4,4,r) +7/256*sin(4*phi)*R(6,4,r) +9/1280*sin(4*phi)*R(8,4,r) +1/1280*sin(4*phi)*R(10,4,r) +9/256*sin(2*phi)*R(2,2,r) +15/512*sin(2*phi)*R(4,2,r) +7/512*sin(2*phi)*R(6,2,r) +9/2560*sin(2*phi)*R(8,2,r) +1/2560*sin(2*phi)*R(10,2,r) X^8*Y^2 = -1/512*R(10,10,r)*cos(10*phi) -27/2560*cos(8*phi)*R(8,8,r) -3/2560*cos(8*phi)*R(10,8,r) -91/4608*cos(6*phi)*R(6,6,r) -13/2560*cos(6*phi)*R(8,6,r) -13/23040*cos(6*phi)*R(10,6,r) -5/512*cos(4*phi)*R(4,4,r) -7/1536*cos(4*phi)*R(6,4,r) -3/2560*cos(4*phi)*R(8,4,r) -1/7680*cos(4*phi)*R(10,4,r) +3/256*cos(2*phi)*R(2,2,r) +5/512*cos(2*phi)*R(4,2,r) +7/1536*cos(2*phi)*R(6,2,r) +3/2560*cos(2*phi)*R(8,2,r) +1/7680*cos(2*phi)*R(10,2,r) +7/1536*R(0,0,r) +5/512*R(2,0,r) +25/3072*R(4,0,r) +35/9216*R(6,0,r) +1/1024*R(8,0,r) +1/9216*R(10,0,r) X^7*Y^3 = -1/512*R(10,10,r)*sin(10*phi) -9/1280*sin(8*phi)*R(8,8,r) -1/1280*sin(8*phi)*R(10,8,r) -7/1536*sin(6*phi)*R(6,6,r) -3/2560*sin(6*phi)*R(8,6,r) -1/7680*sin(6*phi)*R(10,6,r) +5/512*sin(4*phi)*R(4,4,r) +7/1536*sin(4*phi)*R(6,4,r) +3/2560*sin(4*phi)*R(8,4,r) +1/7680*sin(4*phi)*R(10,4,r) +3/256*sin(2*phi)*R(2,2,r) +5/512*sin(2*phi)*R(4,2,r) +7/1536*sin(2*phi)*R(6,2,r) +3/2560*sin(2*phi)*R(8,2,r) +1/7680*sin(2*phi)*R(10,2,r) X^6*Y^4 = 1/512*R(10,10,r)*cos(10*phi) +9/2560*cos(8*phi)*R(8,8,r) +1/2560*cos(8*phi)*R(10,8,r) -7/1536*cos(6*phi)*R(6,6,r) -3/2560*cos(6*phi)*R(8,6,r) -1/7680*cos(6*phi)*R(10,6,r) -5/512*cos(4*phi)*R(4,4,r) -7/1536*cos(4*phi)*R(6,4,r) -3/2560*cos(4*phi)*R(8,4,r) -1/7680*cos(4*phi)*R(10,4,r) +3/1792*cos(2*phi)*R(2,2,r) +5/3584*cos(2*phi)*R(4,2,r) +1/1536*cos(2*phi)*R(6,2,r) +3/17920*cos(2*phi)*R(8,2,r) +1/53760*cos(2*phi)*R(10,2,r) +1/512*R(0,0,r) +15/3584*R(2,0,r) +25/7168*R(4,0,r) +5/3072*R(6,0,r) +3/7168*R(8,0,r) +1/21504*R(10,0,r) X^5*Y^5 = 1/512*R(10,10,r)*sin(10*phi) -35/4608*sin(6*phi)*R(6,6,r) -1/512*sin(6*phi)*R(8,6,r) -1/4608*sin(6*phi)*R(10,6,r) +15/1792*sin(2*phi)*R(2,2,r) +25/3584*sin(2*phi)*R(4,2,r) +5/1536*sin(2*phi)*R(6,2,r) +3/3584*sin(2*phi)*R(8,2,r) +1/10752*sin(2*phi)*R(10,2,r) X^4*Y^6 = -1/512*R(10,10,r)*cos(10*phi) +9/2560*cos(8*phi)*R(8,8,r) +1/2560*cos(8*phi)*R(10,8,r) +7/1536*cos(6*phi)*R(6,6,r) +3/2560*cos(6*phi)*R(8,6,r) +1/7680*cos(6*phi)*R(10,6,r) -5/512*cos(4*phi)*R(4,4,r) -7/1536*cos(4*phi)*R(6,4,r) -3/2560*cos(4*phi)*R(8,4,r) -1/7680*cos(4*phi)*R(10,4,r) -3/1792*cos(2*phi)*R(2,2,r) -5/3584*cos(2*phi)*R(4,2,r) -1/1536*cos(2*phi)*R(6,2,r) -3/17920*cos(2*phi)*R(8,2,r) -1/53760*cos(2*phi)*R(10,2,r) +1/512*R(0,0,r) +15/3584*R(2,0,r) +25/7168*R(4,0,r) +5/3072*R(6,0,r) +3/7168*R(8,0,r) +1/21504*R(10,0,r) X^3*Y^7 = -1/512*R(10,10,r)*sin(10*phi) +9/1280*sin(8*phi)*R(8,8,r) +1/1280*sin(8*phi)*R(10,8,r) -7/1536*sin(6*phi)*R(6,6,r) -3/2560*sin(6*phi)*R(8,6,r) -1/7680*sin(6*phi)*R(10,6,r) -5/512*sin(4*phi)*R(4,4,r) -7/1536*sin(4*phi)*R(6,4,r) -3/2560*sin(4*phi)*R(8,4,r) -1/7680*sin(4*phi)*R(10,4,r) +3/256*sin(2*phi)*R(2,2,r) +5/512*sin(2*phi)*R(4,2,r) +7/1536*sin(2*phi)*R(6,2,r) +3/2560*sin(2*phi)*R(8,2,r) +1/7680*sin(2*phi)*R(10,2,r) X^2*Y^8 = 1/512*R(10,10,r)*cos(10*phi) -27/2560*cos(8*phi)*R(8,8,r) -3/2560*cos(8*phi)*R(10,8,r) +91/4608*cos(6*phi)*R(6,6,r) +13/2560*cos(6*phi)*R(8,6,r) +13/23040*cos(6*phi)*R(10,6,r) -5/512*cos(4*phi)*R(4,4,r) -7/1536*cos(4*phi)*R(6,4,r) -3/2560*cos(4*phi)*R(8,4,r) -1/7680*cos(4*phi)*R(10,4,r) -3/256*cos(2*phi)*R(2,2,r) -5/512*cos(2*phi)*R(4,2,r) -7/1536*cos(2*phi)*R(6,2,r) -3/2560*cos(2*phi)*R(8,2,r) -1/7680*cos(2*phi)*R(10,2,r) +7/1536*R(0,0,r) +5/512*R(2,0,r) +25/3072*R(4,0,r) +35/9216*R(6,0,r) +1/1024*R(8,0,r) +1/9216*R(10,0,r) X*Y^9 = 1/512*R(10,10,r)*sin(10*phi) -9/640*sin(8*phi)*R(8,8,r) -1/640*sin(8*phi)*R(10,8,r) +21/512*sin(6*phi)*R(6,6,r) +27/2560*sin(6*phi)*R(8,6,r) +3/2560*sin(6*phi)*R(10,6,r) -15/256*sin(4*phi)*R(4,4,r) -7/256*sin(4*phi)*R(6,4,r) -9/1280*sin(4*phi)*R(8,4,r) -1/1280*sin(4*phi)*R(10,4,r) +9/256*sin(2*phi)*R(2,2,r) +15/512*sin(2*phi)*R(4,2,r) +7/512*sin(2*phi)*R(6,2,r) +9/2560*sin(2*phi)*R(8,2,r) +1/2560*sin(2*phi)*R(10,2,r) Y^10 = -1/512*R(10,10,r)*cos(10*phi) +9/512*cos(8*phi)*R(8,8,r) +1/512*cos(8*phi)*R(10,8,r) -35/512*cos(6*phi)*R(6,6,r) -9/512*cos(6*phi)*R(8,6,r) -1/512*cos(6*phi)*R(10,6,r) +75/512*cos(4*phi)*R(4,4,r) +35/512*cos(4*phi)*R(6,4,r) +9/512*cos(4*phi)*R(8,4,r) +1/512*cos(4*phi)*R(10,4,r) -45/256*cos(2*phi)*R(2,2,r) -75/512*cos(2*phi)*R(4,2,r) -35/512*cos(2*phi)*R(6,2,r) -9/512*cos(2*phi)*R(8,2,r) -1/512*cos(2*phi)*R(10,2,r) +21/512*R(0,0,r) +45/512*R(2,0,r) +75/1024*R(4,0,r) +35/1024*R(6,0,r) +9/1024*R(8,0,r) +1/1024*R(10,0,r)