20 Jul
2017
20 Jul
'17
1:28 p.m.
has polynomials in x as coefficients of (q-1)^n. See gosper.org/psi_q.png Plots are blue digamma overwritten by gold series approximation. For (q-)PolyGamma[n,...], just d^n/dx^n. QPolyGamma[3, 1/2, q] is phenomenally near π⁴ for .1<q<1: Table[QPolyGamma[3, 1/2, q] - π⁴, {q, .1`69, .9`69, .1`69}] // N Out[1343]= {-0.0000557992067391662, -3.46554182307681*10^-8, -8.95673115069408*10^-12, -3.02779751180959*10^-16, -2.86641755545745*10^-22, -4.2550061594941*10^-31, -1.32744226211741*10^-45, -1.41336365314375*10^-65} Intermediate 69 digit precision because of huge subtractive significance loss, as well as some sub-par Mathematica numerics. --rwg