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unedited_source.txt
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W65[a, b, c, d, q, z], 20] == 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}]
W87[a, b, c, d, e, f, q, z] == Sum[QPh[{Sqrt[q] a^(3/2)/(b c), Sqrt[q a]/b, Sqrt[q a]/c, q a/(b c), d, e, f}, q, n]/ QPh[{q, Sqrt[q a], q a/b, q a/c, q a/d, q a/e, q a/f}, q, n] QPh[{q a}, q, 2 n]/ QPh[{Sqrt[q] a^(3/2)/(b c)}, q, 2 n] (b c z/Sqrt[q a])^n W76[ q^(2 n) a, b c/Sqrt[q a], q^n d, q^n e, q^n f, q, z], {n, 0, Infinity}]
W87[a, b, c, d, e, f, q, z] == Sum[QPh[{Sqrt[q] a^(3/2)/(b c), Sqrt[q a]/b, Sqrt[q a]/c, q a/(b c), d, e, f}, q, n]/ QPh[{q, Sqrt[q a], q a/b, q a/c, q a/d, q a/e, q a/f}, q, n] QPh[{q a}, q, 2 n]/ QPh[{Sqrt[q] a^(3/2)/(b c)}, q, 2 n] (b c z/Sqrt[q a])^n Sum[ QPh[{(a^2 q^(1 + 2 n))/(b c d), (a q^(1 + n))/(b c), Sqrt[a q]/ d, (q^n (a q)^(3/2))/(b c d), e q^n, f q^n}, q, m]/ QPh[{q, q^n Sqrt[a q], (q^(2 n) (a q)^(3/2))/(b c), ( a q^(1 + n))/d, (a q^(1 + n))/e, (a q^(1 + n))/f}, q, m] QPh[{a q^(1 + 2 n)}, q, 2 m]/ QPh[{(a^2 q^(1 + 2 n))/(b c d)}, q, 2 m] ((b c d z)/(a q))^ m W65[a q^(2 (m + n)), (b c d)/(a q), e q^(m + n), f q^(m + n), q, z], {m, 0, Infinity}], {n, 0, Infinity}]
W87[a, b, c, d, e, f, q, z] == Sum[QPh[{Sqrt[q] a^(3/2)/(b c), Sqrt[q a]/b, Sqrt[q a]/c, q a/(b c), d, e, f}, q, n]/ QPh[{q, Sqrt[q a], q a/b, q a/c, q a/d, q a/e, q a/f}, q, n] QPh[{q a}, q, 2 n]/ QPh[{Sqrt[q] a^(3/2)/(b c)}, q, 2 n] (b c z/Sqrt[q a])^n Sum[ QPh[{(a^2 q^(1 + 2 n))/(b c d), (a q^(1 + n))/(b c), Sqrt[a q]/ d, (q^n (a q)^(3/2))/(b c d), e q^n, f q^n}, q, m]/ QPh[{q, q^n Sqrt[a q], (q^(2 n) (a q)^(3/2))/(b c), ( a q^(1 + n))/d, (a q^(1 + n))/e, (a q^(1 + n))/f}, q, m] QPh[{a q^(1 + 2 n)}, q, 2 m]/ QPh[{(a^2 q^(1 + 2 n))/(b c d)}, q, 2 m] ((b c d z)/(a q))^ m QPhI[{q, (b^2 c^2 d^2 e^2 f^2 z^2)/(a^4 q^4), a q^(1 + 2 (m + n)), (q^(m + n) (a q)^(5/2))/(b c d e f)}, q]/(2 \[Pi] QPhI[{f, q/f, (q^(m + n) (a q)^(5/2))/( b c d e z), (b c d e q^(-(3/2) - m - n) z)/a^(5/2), ( b^2 c^2 d^2 e^2 f^2 z^2)/(a^4 q^3), (a q^(1 + m + n))/f, ( q^(2 (m + n)) (a q)^(5/2))/(b c d e)}, q]) Sum[ q^(1/2 (-1 + j) j) QPh[{(a^(5/2) q^(3/2 + 2 m + 2 n))/(b c d e), ( q^(m + n) (a q)^(3/2))/(b c d), Sqrt[a q]/e, ( a^2 q^(2 + m + n))/(b c d e), f q^(m + n)}, q, j]/ QPh[{q, (a^2 q^(2 (1 + m + n)))/(b c d), (a q^(1 + m + n))/e, Sqrt[a q^(1 + 2 (m + n))], (q^(m + n) (a q)^(5/2))/( b c d e f)}, q, j] QPh[{(q^(2 (m + n)) (a q)^(5/2))/(b c d e)}, q, 2 j]/ QPh[{(a^(5/2) q^(3/2 + 2 m + 2 n))/(b c d e)}, q, 2 j] (-a q^( 1 + m + n))^ j NIntegrate[ QPhI[{( q^(3/4 + j/2 + 1/2 (1 + m + n)) a^(5/4) Sqrt[f] \[Rho])/( Sqrt[b c d e z] g ), ( q^(1/4 - j/2 + 1/2 (-1 - m - n)) Sqrt[b c d e z] \[Rho])/( a^(5/4) Sqrt[f] g), ((q^(3/4 + j/2 + 1/2 (1 + m + n))) (a^( 5/4)) Sqrt[f] g )/( Sqrt[b c d e z] \[Rho]), ((q^( 1/4 - j/2 + 1/2 (-1 - m - n))) Sqrt[b c d e z] g )/( a^(5/4) Sqrt[f] \[Rho]), ((q^( 1/4 + j/2 + 1/2 (-1 + m + n))) Sqrt[b c d e z] g )/( a^(1/4) Sqrt[f] \[Rho]), ((q^( 1/4 (-7 + 2 j + 2 m + 2 n))) ((b c d e f z)^(3/2)) g )/( a^(11/4) \[Rho]), ((q^( 3/4 + (3 j)/2 + 1/2 (1 + 3 (m + n)))) (a^(5/4)) Sqrt[f z] g )/(Sqrt[b c d e] \[Rho])}, q]/ QPhI[{(q^(3/4 + j/2 + 1/2 (1 + m + n)) a^(5/4) \[Rho])/( Sqrt[b c d e f z] g ), ( q^(-(3/4) - j/2 + 1/2 (-1 - m - n)) Sqrt[ b c d e f z] \[Rho])/( a^(5/4) g), ((q^(1/4 (-1 + 2 j + 2 m + 2 n))) Sqrt[ b c d e f z] g )/( a^(3/4) \[Rho]), ((q^(1/4 (-3 + 2 j + 2 m + 2 n))) Sqrt[ b c d e f z] g )/( a^(3/4) \[Rho]), -(( (q^(1/4 (-3 + 2 j + 2 m + 2 n))) Sqrt[ b c d e f z] g )/(a^(3/4) \[Rho])), -(( q^(1/4 (-1 + 2 j + 2 m + 2 n)) Sqrt[b c d e f z] g)/( a^(3/4) \[Rho])), ((q^(3/4 + j/2 + 1/2 (1 + m + n))) (a^( 5/4)) Sqrt[z] g )/(Sqrt[b c d e f] \[Rho])}, q], {\[Zeta], -Pi, Pi}, WorkingPrecision -> 30], {j, 0, Infinity}], {m, 0, Infinity}], {n, 0, Infinity}]