#Maple file with some explicit coefficients of the expansions useful for computing
#the nodes and weights of the Gauss-Jacobi quadratures.
#The expansions are given in the paper "Non-iterative computation of Gauss-Jacobi quadrature",
#by Amparo Gil, Javier Segura and Nico M. Temme
#---------------------------------------------------------------------------------
# If more coefficients are nedeed, please contact with the authors.
#--------------------------------------------------------------------------------- 
#a) Expansion (2.26), theta_0, theta_1, theta_2, theta_3
# n is the degree of the Jacobi polynomial,
# a is the alpha parameter, b is the beta parameter

kappa:= n+(a+b+1)/2; kappa2:= kappa^2;
thetak[0]:= evalf((n+1-k+a/2-1/4)*Pi/kappa); 
x:= cos(thetak[0]);
sintheta:= sqrt(1-x^2);
thetak[1]:= -(1/8)*(2*b^2*x+2*a^2*x-x-2*b^2+2*a^2)/sintheta;
thetak[2]:= (1/384)*(-33*x-36*b^2*x^2+36*a^2*x^2+24*b^4*x^2-24*a^4*x^2+84*b^2*x-60*a^4*x-60*b^4*x+84*a^2*x+4*b^4*x^3+4*a^4*x^3-8*b^2*x^3-8*a^2*x^3+40*a^2-40*b^2+32*b^4-32*a^4+2*x^3+24*a^2*b^2*x^3-24*a^2*b^2*x)/sintheta^3;
thetak[3]:= -(1/15360)*(520*a^4*b^2*x-760*a^4*b^2*x^3-80*a^4*b^2*x^4-120*a^4*b^2*x^2+80*a^2*b^4*x^4+120*a^2*b^4*x^2+520*a^2*b^4*x-760*a^2*b^4*x^3-2595*x-7120*b^2*x^2+7120*a^2*x^2+6320*b^4*x^2-6320*a^4*x^2+6690*b^2*x-5980*a^4*x-5980*b^4*x+6690*a^2*x-2460*b^4*x^3+280*b^4*x^4-280*a^4*x^4-2460*a^4*x^3+200*a^4*b^2-200*a^2*b^4+1960*a^6*x^2+80*a^6*x^4+1880*a^6*x+760*a^6*x^3+1880*b^6*x+760*b^6*x^3-80*b^6*x^4-1960*b^6*x^2+2720*b^2*x^3+2720*a^2*x^3-370*b^2*x^4+370*a^2*x^4+112*b^2*x^5+112*a^2*x^5-80*b^4*x^5-80*a^4*x^5+16*a^6*x^5+16*b^6*x^5+2032*a^2-2032*b^2+1920*b^4-1920*a^4-1160*x^3+616*a^6-616*b^6-24*x^5+240*a^4*b^2*x^5+240*a^2*b^4*x^5+1720*a^2*b^2*x^3-1240*a^2*b^2*x-480*a^2*b^2*x^5)/sintheta^5;

# b) Expansion (2.20), M, N coefficients (first three terms of the expansions for M and N)
#    s=sin(theta), x=cos(theta) theta obtained using the asymptotic approximation for the zeros
mk[0]:= 1;
nk[1]:= (1/8)*(2*a^2*x+2*b^2*x-2*b^2+2*a^2-x)/s;
mk[2]:= -(1/384)*(-24+16*a-24*a^2*b^2-48*a*b^2+48*a^2+48*b^2+12*a^4+12*b^4-16*a^3+3*x^2+12*a^4*x^2+12*b^4*x^2-12*b^2*x^2-12*a^2*x^2+16*a^3*x^2-16*x^2*a+36*a^2*x-36*b^2*x+24*a^4*x-24*b^4*x+24*a^2*b^2*x^2+48*b^2*x^2*a)/s^2;
nk[3]:= -(1/3072)*(-32*a*b^2-24*a^4*b^2+24*a^2*b^4-64*a^3*b^2+96*a*b^4-208*a^2+208*b^2+32*a^4-32*b^4+32*a^3+8*a^6-8*b^6-32*a^5+192*x-384*a^2*x-384*b^2*x+15*x^3-58*b^2*x^3-58*a^2*x^3-24*b^6*x^2+8*b^6*x^3+24*b^6*x+8*a^6*x^3+24*a^6*x+24*a^6*x^2+20*b^4*x^3+20*a^4*x^3-48*a^3*x^3+32*a^5*x^3+32*a^5*x^2-32*a^5*x+48*a^3*x+16*x^3*a-16*x*a-24*a^2*b^4*x-24*a^2*b^4*x^2+168*a^2*b^2*x^3+80*b^2*x*a+24*a^4*b^2*x^2-96*b^4*x^2*a+24*a^2*b^4*x^3-168*a^2*b^2*x-24*a^4*b^2*x+24*a^4*b^2*x^3+64*a^3*b^2*x^2+96*b^4*x^3*a-128*a^3*x*b^2-80*b^2*x^3*a+128*a^3*x^3*b^2-96*b^4*x*a+234*b^2*x^2-234*a^2*x^2+72*a^4*x^2-72*b^4*x^2+84*a^4*x+84*b^4*x-32*a^3*x^2+32*b^2*x^2*a)/s^3;
mk[4]:= 
(1/1474560)*(-54720+6912*a-32640*a^2*b^2-26880*a*b^2+9600*a^4*b^2+13440*a^2*b^4-960*a^6*b^2+1440*a^4*b^4-960*a^2*b^6+11520*a^3*b^2+9600*a^3*b^4+1920*a*b^4-1920*a^5*b^2-5760*a*b^6+128000*a^2+126720*b^2-59200*a^4-56640*b^4-3840*a^3-640*a^6-1920*b^6+240*a^8+240*b^8-1920*a^7-1152*a^5+297600*a^2*x-297600*b^2*x-945*x^4-33840*a^2*b^2*x^4+9600*a^5*b^2*x^4-7680*a^5*x^2*b^2+11520*a^5*b^2*x^3+1440*a^4*b^4*x^4+960*a^2*b^6*x^4+34560*a^3*b^2*x^4-11520*b^6*x^3*a-3840*a^3*b^4*x^3+1920*a^2*b^6*x+33120*a^4*b^2*x^4+5760*b^6*x^4*a-23040*a^3*b^4*x^2-11520*a^5*x*b^2-2880*a^4*b^4*x^2+1920*a^6*b^2*x^3+36960*a^2*b^4*x^4+15360*b^4*x^4*a-42720*b^2*x^4*a+960*a^6*b^2*x^4-1920*a^6*b^2*x+3840*a^3*b^4*x+13440*a^3*b^4*x^4-1920*a^2*b^6*x^3+11520*b^6*x*a+1440*a^8*x^2-960*b^8*x+960*a^8*x^3+960*a^8*x+240*a^8*x^4+1440*b^8*x^2-960*b^8*x^3+240*b^8*x^4+5640*b^2*x^4+6920*a^2*x^4+3360*b^6*x^4+4640*a^6*x^4-9240*b^4*x^4-11800*a^4*x^4+3840*a^7*x^3-12960*a^3*x^4+1920*a^7*x^4+768*a^5*x^4+10272*x^4*a-3840*a^7*x-60840*b^2*x^3+60840*a^2*x^3+4320*b^6*x^2-8160*b^6*x^3+2400*b^6*x+8160*a^6*x^3-2400*a^6*x+1760*a^6*x^2+35760*b^4*x^3-35760*a^4*x^3-5760*a^3*x^3+1920*a^5*x^3+384*a^5*x^2-1920*a^5*x+5760*a^3*x+23520*a^2*b^4*x-50400*a^2*b^4*x^2-5760*b^2*x*a-42720*a^4*b^2*x^2-17280*b^4*x^2*a-23520*a^2*b^4*x^3-23520*a^4*b^2*x+23520*a^4*b^2*x^3-46080*a^3*b^2*x^2-13440*b^4*x^3*a-11520*a^3*x*b^2+5760*b^2*x^3*a+11520*a^3*x^3*b^2+13440*b^4*x*a+226080*b^2*x^2+223520*a^2*x^2-95320*a^4*x^2-100440*b^4*x^2-130560*a^4*x+130560*b^4*x+16800*a^3*x^2-17184*x^2*a-102960*x^2+69600*b^2*x^2*a+66480*a^2*b^2*x^2)/s^4;
nk[5]:= (1/11796480)*(-2560*a^2*b^2+11776*a*b^2+45440*a^4*b^2-40320*a^2*b^4+20480*a^6*b^2+7680*a^4*b^4-30720*a^2*b^6+5120*a^3*b^2-37120*a^3*b^4-12800*a*b^4+63744*a^5*b^2-32000*a*b^6+7680*a^5*b^4-10240*a^3*b^6+3840*b^8*a-960*a^4*b^6+960*a^6*b^4-480*a^8*b^2+480*a^2*b^8-1267584*a^2+1267584*b^2+716800*a^4-714240*b^4-11776*a^3-83072*a^6+77952*b^6-1280*a^8+3840*b^8+5376*a^7+7680*a^5-96*b^10+96*a^10-1280*a^9+1753920*x-4073600*a^2*x-4072320*b^2*x-2560*a^2*b^2*x^4+113664*a^5*b^2*x^4-177408*a^5*x^2*b^2-218112*a^5*b^2*x^3+7680*a^4*b^4*x^4-74880*a^2*b^6*x^4-136320*a^3*b^2*x^4-64000*b^6*x^3*a-419840*a^3*b^4*x^3+8640*a^2*b^6*x+3920*a^4*b^2*x^4-76800*b^6*x^4*a+90880*a^3*b^4*x^2+84096*a^5*x*b^2-15360*a^4*b^4*x^2-51200*a^6*b^2*x^3+1200*a^2*b^4*x^4+216000*b^4*x^4*a-58944*b^2*x^4*a+64640*a^6*b^2*x^4+3520*a^6*b^2*x+201600*a^3*b^4*x-53760*a^3*b^4*x^4-61440*a^2*b^6*x^3+9600*b^6*x*a-13760*a^8*x^2-11760*b^8*x+1120*a^8*x^3-9200*a^8*x+13120*a^8*x^4+8640*b^8*x^2+6240*b^8*x^3-10560*b^8*x^4+230850*b^2*x^4-230850*a^2*x^4+31920*b^6*x^4-37040*a^6*x^4-98640*b^4*x^4+101200*a^4*x^4-10752*a^7*x^3+58944*a^3*x^4+16896*a^7*x^4-79680*a^5*x^4-384*a^7*x+876960*x^3-2065920*b^2*x^3-2063360*a^2*x^3+337680*b^6*x^2-179760*b^6*x^3-268800*b^6*x-166960*a^6*x^3-275200*a^6*x-327440*a^6*x^2+1202760*b^4*x^3+1192520*a^4*x^3+6752*a^3*x^3+8256*a^5*x^3+72000*a^5*x^2+39552*a^5*x-55296*a^3*x-6816*x^3*a+19968*x*a+149760*a^2*b^4*x+39120*a^2*b^4*x^2+323440*a^2*b^2*x^3-86016*b^2*x*a-49360*a^4*b^2*x^2-203200*b^4*x^2*a-258000*a^2*b^4*x^3+10240*a^2*b^2*x+148480*a^4*b^2*x-255440*a^4*b^2*x^3+131200*a^3*b^2*x^2+63680*b^4*x^3*a+49920*a^3*x*b^2+1952*b^2*x^3*a+183040*a^3*x^3*b^2+82560*b^4*x*a+4557600*b^2*x^2-4557600*a^2*x^2+2614720*a^4*x^2-2619840*b^4*x^2+2286080*a^4*x+2280960*b^4*x-47168*a^3*x^2+47168*b^2*x^2*a+5120*a^2*b^2*x^2+960*a^6*b^4*x^4-1920*a^6*b^4*x^3+84064*b^2*x^5*a-146240*b^4*x^5*a+7680*a^7*b^2*x^5+134016*a^5*b^2*x^5+218240*a^3*b^4*x^5+12800*a^3*b^6*x^5-15360*a^7*x^2*b^2+25600*a^3*b^6*x^2+15360*a^5*x*b^4-30720*a^5*b^4*x^3+15360*a^7*b^2*x^4-7680*a^7*b^2*x+7680*a^5*b^4*x^4-15360*a^5*b^4*x^2-15360*a^3*b^6*x^4+7680*a^3*b^6*x-20480*a^3*b^6*x^3-11520*b^8*x*a+7680*b^8*x^2*a+7680*b^8*x^3*a-11520*b^8*x^4*a+108800*b^6*x^2*a+480*a^8*b^2*x^5+960*a^4*b^6*x^5+3840*b^8*x^5*a+1440*a^8*b^2*x^4+960*a^4*b^6*x+47680*a^6*b^2*x^5+108240*a^2*b^4*x^5+960*a^2*b^8*x^2-1440*a^8*b^2*x-1440*a^2*b^8*x^4+480*a^2*b^8*x^5+105600*a^2*b^6*x^2+960*a^6*b^4*x^5+106960*a^4*b^2*x^5-960*a^8*b^2*x^2+15360*a^5*b^4*x^5-1440*a^2*b^8*x-1920*a^4*b^6*x^3-333680*a^2*b^2*x^5+1920*a^4*b^6*x^2+90720*a^4*b^4*x^5-1920*a^6*b^4*x^2+90720*a^4*b^4*x+960*a^2*b^8*x^3+960*a^8*b^2*x^3+960*a^6*b^4*x-85120*a^6*b^2*x^2+52800*a^2*b^6*x^5-232960*a^3*b^2*x^5-181440*a^4*b^4*x^3-960*a^4*b^6*x^4+54400*b^6*x^5*a-17955*x^5+960*a^10*x^2+96*a^10*x^5+960*a^10*x^3+480*a^10*x+480*a^10*x^4+480*b^10*x-960*b^10*x^2+960*b^10*x^3+96*b^10*x^5-480*b^10*x^4+82206*b^2*x^5+80926*a^2*x^5-51000*b^4*x^5-45880*a^4*x^5-13152*x^5*a+1280*a^9*x^5+11136*a^7*x^5+48544*a^3*x^5-47808*a^5*x^5-2560*a^9*x^2+2560*a^9*x^3-3840*a^9*x+3840*a^9*x^4-22272*a^7*x^2+6160*a^8*x^5+3600*b^8*x^5+1008*b^6*x^5-5392*a^6*x^5)/s^5;

#c) Expansion (3.15), theta_1, theta_2
# alpha, beta, parameters of the Jacobi polynomial
# s=sin(theta0), c=cos(theta0), t=theta0

Sk[0]:= 1;
Tk[0]:= -(1/8)*(2*c*t*beta^2-c*t+2*alpha^2*c*t-4*alpha^2*s+s-2*t*beta^2+2*alpha^2*t)/(s*t);
Sk[1]:= -(1/384)*(-45-48*alpha-96*alpha*t*beta^2*s*c-48*t*alpha^2*beta^2*s*c-12*alpha^2*c*t*s+48*s*c*t*alpha-96*alpha^3*c*t*s-48*alpha^4*c*t*s-24*beta^4*c*t^2-36*alpha^2*t*s-96*alpha^3*t*s-48*alpha^4*t*s+36*t*beta^2*s+12*t^2*beta^4*c^2-12*t^2*beta^2*c^2+60*t^2*beta^2*c+24*alpha^4*t^2*c-60*t^2*alpha^2*c+24*t^2-48*t^2*alpha^2+12*alpha^4*t^2-24*t^2*alpha^2*beta^2-48*t^2*alpha*beta^2+12*t^2*beta^4-48*t^2*beta^2-48*alpha^4*c^2-192*alpha^3*c^2+48*c^2*alpha+18*s*c*t-16*alpha*c^2*t^2-12*alpha^2*c^2*t^2+16*alpha^3*c^2*t^2+12*alpha^4*c^2*t^2+3*c^2*t^2+16*t^2*alpha-16*alpha^3*t^2-168*alpha^2*c^2+45*c^2+48*alpha^4+192*alpha^3+96*alpha*t*beta^2*s+48*t*alpha^2*beta^2*s+24*t^2*alpha^2*beta^2*c^2+48*t^2*alpha*beta^2*c^2-36*t*beta^2*s*c+168*alpha^2)/(t^2*s^2);
Tk[1]:= (1/3072)*(225*s+16*alpha*c^3*t^3-58*alpha^2*c^3*t^3-48*alpha^3*c^3*t^3+20*alpha^4*c^3*t^3+32*alpha^5*c^3*t^3-240*t*alpha^2*beta^2*c^2+96*alpha^4*t*beta^2*c^2+240*t*alpha^2*beta^2*c^3-240*t*alpha^2*beta^2*c-96*alpha^4*t*beta^2*c^3+96*alpha^4*t*beta^2*c+96*alpha^6*t+168*t^2*alpha^2*beta^2*s-48*t^2*alpha*beta^2*s+12*t^2*beta^4*s*c^2-12*t^2*beta^2*s*c^2+192*t^2*alpha^3*beta^2*s+96*alpha^4*t^2*beta^2*s-48*alpha^2*t^2*beta^4*s+80*t^3*alpha*beta^2*c-80*t^3*alpha*beta^2*c^3-168*t^3*alpha^2*beta^2*c+168*t^3*alpha^2*beta^2*c^3-128*t^3*alpha^3*beta^2*c+128*t^3*alpha^3*beta^2*c^3-96*t^3*beta^4*alpha*c+96*t^3*beta^4*alpha*c^3-24*t^3*alpha^4*beta^2*c+24*t^3*alpha^4*beta^2*c^3-24*t^3*beta^4*alpha^2*c+24*t^3*beta^4*alpha^2*c^3+32*t^3*alpha*beta^2*c^2+64*t^3*alpha^3*beta^2*c^2-96*t^3*beta^4*alpha*c^2+24*t^3*alpha^4*beta^2*c^2-24*t^3*beta^4*alpha^2*c^2-96*alpha^6*t^2*s*c-60*t^2*alpha^2*s*c+264*alpha^4*t^2*s*c-24*t^2*beta^4*s*c+60*t^2*beta^2*s*c+8*beta^6*c^3*t^3+24*beta^6*c*t^3-64*alpha^6*s-48*alpha^6*t^2*s+64*alpha^5*t^2*s-144*t^2*alpha^2*s+204*alpha^4*t^2*s+12*t^2*beta^4*s-48*t^2*beta^2*s+16*t^2*alpha*s-80*alpha^3*t^2*s-300*alpha^4*t^3*c-300*t^3*beta^4*c+20*t^3*beta^4*c^3+576*t^3*beta^2*c-58*t^3*beta^2*c^3+24*alpha^6*t^3*c+576*alpha^2*t^3*c+48*t^3*alpha^3*c-16*t^3*alpha*c-32*t^3*alpha^5*c-120*alpha^4*t^3*c^2+120*t^3*beta^4*c^2-246*t^3*beta^2*c^2-24*t^3*beta^6*c^2+24*alpha^6*t^3*c^2+246*alpha^2*t^3*c^2-32*t^3*alpha^3*c^2+32*t^3*alpha^5*c^2+240*t*alpha^2*beta^2+1036*s*c^2*alpha^2-560*alpha^4*c^2*s+72*t^2*alpha^2*beta^2*s*c^2+48*t^2*alpha*beta^2*s*c^2-192*t^2*alpha^3*beta^2*s*c^2-96*alpha^4*t^2*beta^2*s*c^2-48*alpha^2*t^2*beta^4*s*c^2-240*t^2*alpha^2*beta^2*s*c+96*alpha^2*t^2*beta^4*s*c+174*alpha^2*c*t-54*alpha^2*c^2*t+54*t*beta^2*c^2+54*c*t*beta^2+3*s*c^2*t^2+54*alpha^2*t-54*t*beta^2+27*c^3*t+24*s*t^2-225*s*c^2-240*alpha^4*t-96*alpha^4*t*beta^2+64*alpha^6*s*c^2-27*c*t-174*c^3*t*alpha^2-288*alpha^4*c*t+240*alpha^4*c^2*t+288*alpha^4*c^3*t+96*alpha^6*c*t-96*alpha^6*c^2*t-96*alpha^6*c^3*t-54*t*beta^2*c^3+80*alpha^3*s*c^2*t^2-16*s*alpha*c^2*t^2-24*alpha^2*s*c^2*t^2+60*alpha^4*s*c^2*t^2-64*alpha^5*s*c^2*t^2-48*alpha^6*s*c^2*t^2-1036*alpha^2*s+15*c^3*t^3-240*t^3*c+8*alpha^6*c^3*t^3-160*alpha^4*t^3+160*t^3*beta^4-272*t^3*beta^2-8*t^3*beta^6+8*alpha^6*t^3-32*t^3*alpha*beta^2-64*t^3*alpha^3*beta^2+96*t^3*beta^4*alpha-24*t^3*alpha^4*beta^2+24*t^3*beta^4*alpha^2+272*alpha^2*t^3+32*t^3*alpha^3-32*t^3*alpha^5+560*alpha^4*s)/(s^3*t^3);
Tkd1[0]:= (1/8)*(2*t^2*beta^2-t^2+2*t^2*alpha^2-4*alpha^2+1-2*c*t^2*beta^2+2*c*t^2*alpha^2+4*c^2*alpha^2-c^2)/(s^2*t^2);

thetak[1]:=  Tk[0];
thetak[2]:= -(1/6)*(6*Tk[0]^2*alpha+6*t*Tk[0]*Sk[1]-6*t*Tk[1]+3*Tk[0]^2+2*t*Tk[0]^3-6*t*Tk[0]*Tkd1[0])/t;


# d) Expansion (3.10), Y, Z coefficients (first two terms of the expansions for Y and Z)
#    t=theta, s=sin(theta), x=cos(theta), theta obtained using the asymptotic approximation for the zeros
Yk[0]:= 1;

Zk[0]:= -(1/4)*(-8*a*s-3*s+2*a^2*x*t+2*x*t*b^2-x*t+2*a^2*t-4*a^2*s-2*t*b^2)/s;

Yk[1]:= -(1/384)*(27-24*t^2-120*a^2+16*t^2*a-16*a^3*t^2+12*a^4*t^2+48*t^2*a^2+12*t^2*b^4+48*t^2*b^2-24*t^2*a^2*b^2-48*t^2*a*b^2+48*a^4-27*x^2-48*a^4*x^2+3*x^2*t^2+120*a^2*x^2+48*t*a^2*b^2*s+24*t^2*a^2*b^2*x^2+48*t^2*a*b^2*x^2+12*t*b^2*s*x-48*a^4*s*x*t+36*a^2*s*x*t-48*t*a^2*b^2*s*x-24*b^4*x*t^2-12*t*b^2*s-48*t*a^4*s+12*a^2*t*s+12*t^2*b^4*x^2-12*t^2*b^2*x^2+24*a^4*t^2*x-36*t^2*b^2*x+36*t^2*a^2*x+12*a^4*x^2*t^2-6*s*x*t-16*a*x^2*t^2-12*a^2*x^2*t^2+16*a^3*x^2*t^2)/(t^2*s^2);

Zk[1]:= (1/1536)*(-8*t^3*b^6-32*t^3*b^4+208*t^3*b^2-208*a^2*t^3+32*a^4*t^3+8*a^6*t^3+32*t^3*a^3-32*t^3*a^5+96*t^3*a*b^4+24*t^3*a^2*b^4-24*t^3*a^4*b^2-64*t^3*a^3*b^2-32*t^3*a*b^2+384*t*a^5+96*a^6*t-96*a^4*t*b^2-384*t*a^3*b^2-336*t*a^2*b^2+336*t*a^4-90*a^2*t+90*t*b^2-96*a^3*t+96*a*t*b^2+96*a^2*t^2*b^4*s*x+144*t^2*a^2*b^2*s*x-96*a^4*t^2*b^2*s*x^2-384*t^2*a^3*b^2*s*x^2-48*a^2*t^2*b^4*s*x^2-408*t^2*a^2*b^2*s*x^2-48*t^2*a*b^2*s*x^2-96*t*a*b^2*x^2+288*t^2*a*b^2*x*s+384*t*a^3*b^2*x^2+96*t*a*b^2*x^3+384*t*a^3*b^2*x-384*t*a^3*b^2*x^3-96*s*a*t^2*b^4*x^2+192*s*a*b^4*x*t^2-192*s*a^5*t^2*x-96*s*a*t^2*b^4-315*s-384*s*a^5-400*s*a^4+192*t^3*x+15*x^3*t^3+315*s*x^2-45*x^3*t+72*s*t^2-64*a^6*s+45*x*t+1364*a^2*s-216*a*s-288*a^3*x*t^2*s-36*t^2*b^4*s*x^2+36*t^2*b^2*s*x^2+264*t^2*a^2*b^2*s-240*t^2*a*b^2*s+96*t^3*a*b^4*x^3+24*t^3*a^2*b^4*x^3+24*t^3*a^4*b^2*x^3+128*t^3*a^3*b^2*x^3+168*t^3*a^2*b^2*x^3-80*t^3*a*b^2*x^3-96*a*t*b^2*x+96*a^3*x^2*t-48*a^6*s*x^2*t^2-160*a^5*s*x^2*t^2-116*s*a^4*x^2*t^2+24*s*a*x^2*t^2+152*a^2*s*x^2*t^2+112*a^3*s*x^2*t^2+96*a^4*t*b^2*x^2+336*t*a^2*b^2*x^2-96*a^4*t*b^2*x^3+96*a^4*t*b^2*x-336*t*a^2*b^2*x^3+336*t*a^2*b^2*x-96*a^6*t^2*s*x-216*a^4*t^2*s*x-108*t^2*a^2*s*x+72*t^2*b^4*s*x+108*t^2*b^2*s*x-96*t^3*a*b^4*x^2-24*t^3*a^2*b^4*x^2+24*t^3*a^4*b^2*x^2+64*t^3*a^3*b^2*x^2+32*t^3*a*b^2*x^2-96*t^3*a*b^4*x-24*t^3*a^2*b^4*x-24*t^3*a^4*b^2*x-128*t^3*a^3*b^2*x-168*t^3*a^2*b^2*x+80*t^3*a*b^2*x+96*a^4*t^2*b^2*s+384*t^2*a^3*b^2*s-48*a^2*t^2*b^4*s-384*a^5*x^2*t-384*a^5*x^3*t+258*x^3*t*a^2+90*t*b^2*x^3+96*a^6*x*t-96*a^6*x^2*t-96*a^6*x^3*t+288*a^4*x*t-336*a^4*x^2*t-288*a^4*x^3*t+20*a^4*x^3*t^3+32*a^5*x^3*t^3+8*a^6*x^3*t^3+16*a*x^3*t^3-58*a^2*x^3*t^3-48*a^3*x^3*t^3-1364*s*x^2*a^2+400*a^4*s*x^2-9*s*x^2*t^2-90*t*b^2*x^2+90*a^2*x^2*t+8*b^6*x^3*t^3+24*b^6*x*t^3-234*a^2*t^3*x^2+72*a^4*t^3*x^2+24*a^6*t^3*x^2-32*t^3*a^3*x^2+32*t^3*a^5*x^2+84*t^3*b^4*x-384*t^3*b^2*x-384*a^2*t^3*x+84*a^4*t^3*x+24*a^6*t^3*x+48*t^3*a^3*x-32*t^3*a^5*x-16*t^3*a*x-24*t^3*b^6*x^2-72*t^3*b^4*x^2+234*t^3*b^2*x^2-48*a^6*t^2*s-32*a^5*t^2*s+144*t^2*a*s-400*a^3*t^2*s-100*a^4*t^2*s-176*t^2*a^2*s-36*t^2*b^4*s-144*t^2*b^2*s+20*t^3*b^4*x^3-58*t^3*b^2*x^3+64*a^6*s*x^2-258*a^2*x*t-90*x*t*b^2+384*t*a^5*x+48*a*x*t+384*s*a^5*x^2-960*s*a^3*x^2+216*s*x^2*a+288*x^3*t*a^3-48*x^3*t*a+960*a^3*s-288*a^3*t*x)/(t^2*s^3);