P0 = 1

P1 = x
{tk} : {0.}
{ck} : {2}

P2 = -1/2 + (3*x^2)/2
{tk} : {-0.5773502691896257, 0.5773502691896257}
{ck} : {1., 1.}

P3 = (-3*x)/2 + (5*x^3)/2
{tk} : {-0.7745966692414834, 0., 0.7745966692414834}
{ck} : {0.5555555555555554, 0.8888888888888892, 0.5555555555555554}

P4 = 3/8 - (15*x^2)/4 + (35*x^4)/8
{tk} : {-0.8611363115940525, -0.33998104358485637, 0.3399810435848563, 0.8611363115940526}
{ck} : {0.34785484513745396, 0.6521451548625455, 0.6521451548625464, 0.34785484513745385}

P5 = (15*x)/8 - (35*x^3)/4 + (63*x^5)/8
{tk} : {-0.9061798459386641, -0.538469310105683, 0., 0.538469310105683, 0.9061798459386641}
{ck} : {0.23692688505618917, 0.4786286704993664, 0.5688888888888882, 0.4786286704993666, 0.2369268850561891}

P6 = -5/16 + (105*x^2)/16 - (315*x^4)/16 + (231*x^6)/16
{tk} : {-0.9324695142031522, -0.6612093864662644, -0.23861918608319693, 0.2386191860831969, 0.6612093864662648, 0.9324695142031517}
{ck} : {0.17132449237917033, 0.36076157304813833, 0.46791393457269065, 0.46791393457269165, 0.360761573048138, 0.17132449237917077}

P7 = (-35*x)/16 + (315*x^3)/16 - (693*x^5)/16 + (429*x^7)/16
{tk} : {-0.9491079123427594, -0.7415311855993937, -0.40584515137739724, 0., 0.4058451513773972, 0.7415311855993945, 0.9491079123427585}
{ck} : {0.1294849661688694, 0.2797053914892785, 0.38183005050511765, 0.41795918367346724, 0.38183005050511565, 0.2797053914892774, 0.12948496616886937}

P8 = 35/128 - (315*x^2)/32 + (3465*x^4)/64 - (3003*x^6)/32 + (6435*x^8)/128
{tk} : {-0.960289856497535, -0.7966664774136291, -0.5255324099163279, -0.18343464249564978, 0.18343464249564978, 0.5255324099163291, 0.7966664774136263, 0.9602898564975364}
{ck} : {0.10122853629037686, 0.2223810344533719, 0.3137066458778912, 0.36268378337836776, 0.36268378337837126, 0.3137066458778851, 0.2223810344533737, 0.1012285362903758}

P9 = (315*x)/128 - (1155*x^3)/32 + (9009*x^5)/64 - (6435*x^7)/32 + (12155*x^9)/128
{tk} : {-0.9681602395076255, -0.8360311073266365, -0.6133714327005904, -0.3242534234038088, 0., 0.32425342340380886, 0.6133714327005908, 0.8360311073266349, 0.9681602395076266}
{ck} : {0.0812743883615738, 0.18064816069486103, 0.26061069640293316, 0.312347077040026, 0.3302393550012244, 0.3123470770399875, 0.2606106964029228, 0.1806481606948603, 0.08127438836157443}

P10 = -63/256 + (3465*x^2)/256 - (15015*x^4)/128 + (45045*x^6)/128 - (109395*x^8)/256 + (46189*x^10)/256
{tk} : {-0.9739065285171691, -0.8650633666889882, -0.6794095682990231, -0.43339539412924727, -0.14887433898163122, 0.14887433898163122, 0.43339539412924716, 0.6794095682990247, 0.8650633666889839, 0.9739065285171722}
{ck} : {0.066671344308686, 0.14945134915057953, 0.2190863625159705, 0.26926671931002444, 0.29552422471465234, 0.2955242247148274, 0.2692667193099909, 0.2190863625159874, 0.14945134915058772, 0.06667134430868416}