acb_hypgeom_gamma_taylor
#include <flint/acb_hypgeom.h>Attempts to compute \Gamma(x), or 1/\Gamma(x) if reciprocal is nonzero, with the tabulated Taylor series of 1/\Gamma(1+x) and argument reduction. Returns 1 on success and 0, without changing res, if x or prec is outside the supported range.
The method applies when |\operatorname{Im} x| is small (at most 4 to 10, depending on the precision), |\operatorname{Re} x| is not too large compared to the precision, and the working precision is at most ARB_HYPGEOM_GAMMA_TAB_PREC bits. The Taylor polynomial is evaluated by rectangular splitting with a rigorous bound for the truncation error. See Taylor series of the reciprocal gamma function.
The FLINT team, “acb_hypgeom_gamma_taylor (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_gamma_taylor.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-gamma-taylor,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_gamma\_taylor (acb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_gamma_taylor.html},
note = {Generated 2026-10-20}
}