Algorithm 349: polygamma functions with arbitrary precision [S14]

We consider summations over digamma and polygamma functions, often with summands of the form (+/-1)^n@j(n+p/q)/n^r and (+/-1)^n@j^(^m^)(n+p/q)/n^r, where m, p, q, and r are positive integers. We develop novel general integral representations and present ...

We evaluate a variety of log-cosine integrals, one of which has value a rational multiple of πζ(4), while others evaluate to the form π[aζ(6) + b(3/4)ζ²(3)], where a > 0 is rational and b is 1 or 2, and ζ is the Riemann zeta function. We show that these ...

Expressions for the polygamma function @j^(^k^)(x) for the arguments x=14 and x=14 are given in terms of Bernoulli numbers, Euler numbers, the Riemann zeta function for odd integer arguments, and the related series of reciprocal powers of integers @b(m)...