hard.txt

W65[a, b, c, d, q, z] == QPhI[{q, ((b c d z)/(q a))^2, q a, (q a)^(3/2)/(b c d)}, q]/(2 \[Pi] QPhI[{f, q/f, (f (q a)^(3/2))/(b c d z), ( q b c d  z)/(f (q a)^(3/2)), (b^2 c^2 d^2 z^2)/( q a^2), (q a)/d, (q^(3/2) a^(3/2))/(b c)}, q]) Sum[ q^Binomial[j, 2] QPh[{(Sqrt[q] (a^(3/2)) )/(b c), Sqrt[q a]/b, Sqrt[ q a]/c, (q a)/(b c), d}, q, j]/ QPh[{q, (q a)/b, (q a)/c, Sqrt[q a], (q a)^(3/2)/( b c d)}, q, j] QPh[{( q^(3/2) a^(3/2))/(b c)}, q, 2 j]/ QPh[{(q^(1/2) a^(3/2))/(b c)}, q, 2 j] ((-q a f)/d)^ j NIntegrate[ QPhI[{f q^(j/2 + 3/4) Sqrt[a^(3/2)/(b c d z)] \[Rho]/g, q/f q^(-j/2 - 3/4) Sqrt[(b c d z)/a^(3/2)] \[Rho]/g, f q^(j/2 + 3/4) Sqrt[a^(3/2)/(b c d z)] g/\[Rho], q/f q^(-j/2 - 3/4) Sqrt[(b c d z)/a^(3/2)] g/\[Rho] , q^(j/2 + 1/4) Sqrt[(b c z a^(1/2))/d] g/\[Rho], q^(j/2 - 1/4) (b c d z)^(3/2)/a^(5/4) g/\[Rho], q^(3 j/2 + 3/4) Sqrt[(d z a^(3/2))/(b c)] g/\[Rho] }, q]/QPhI[{q^(j/2 + 3/4) Sqrt[a^(3/2)/(b c d z)] \[Rho] /g, q^(-(j/2) - 3/4) Sqrt[(b c d z)/a^(3/2)] \[Rho]/g, ( q^(j/2 + 1/4) Sqrt[b c d z])/a^(1/4) g/\[Rho], ( q^(j/2 - 1/4) Sqrt[b c d z])/(a^(1/4)) g/\[Rho], -(( q^(j/2 - 1/4) Sqrt[b c d z])/(a^( 1/4)) ) g/\[Rho], -((q^(1/4 + j/2) Sqrt[b c d z])/a^( 1/4)) g/\[Rho], q^(j/2 + 3/4) Sqrt[(a^(3/2) z)/(b c d )] g/\[Rho]}, q], {\[Zeta], -Pi, Pi}, WorkingPrecision -> 20], {j, 0, Infinity}]