acb_polygamma
Synopsis
#include <flint/acb.h>For a nonnegative integer s this is the s-th derivative of the digamma function: s = 0 calls acb_digamma and integers s \ge 1 the Hurwitz zeta function (for small s, reading the coefficients of acb_poly_digamma_series can be faster). Other s use the generalisation of Espinosa and Moll [EM2004],
\psi(s, z) = \frac{\zeta'(s+1, z) + (\gamma + \psi(-s)) \zeta(s+1,
z)}{\Gamma(-s)}.
References#
- [EM2004] O. Espinosa and V. Moll, "A generalized polygamma function", Integral Transforms and Special Functions (2004), 101-115.
Cite this page
The FLINT team, “acb_polygamma (acb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb/acb_polygamma.html (generated 2026-10-20).
@misc{flint-doc-acb-acb-polygamma,
author = {{The FLINT team}},
title = {{acb\_polygamma (acb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb/acb_polygamma.html},
note = {Generated 2026-10-20}
}