acb_barnes_g, acb_log_barnes_g
Synopsis
#include <flint/acb.h>Set res to the Barnes G-function, respectively its logarithm, which has its branch cut on the negative real axis and satisfies \log G(z + 1) = \log \Gamma(z) + \log G(z) for all z.
Small integers use the recurrence G(z + 1) = \Gamma(z) G(z) with G(1) = 1. Otherwise \log G(z) = (z - 1) \log \Gamma(z) - \zeta'(-1, z) + \zeta'(-1).
Cite this page
The FLINT team, “acb_barnes_g, acb_log_barnes_g (acb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb/acb_barnes_g.html (generated 2026-10-20).
@misc{flint-doc-acb-acb-barnes-g,
author = {{The FLINT team}},
title = {{acb\_barnes\_g, acb\_log\_barnes\_g (acb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb/acb_barnes_g.html},
note = {Generated 2026-10-20}
}