FLINT3.7.0-dev
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acb_hypgeom_gamma_taylor

Synopsis#include <flint/acb_hypgeom.h>
int acb_hypgeom_gamma_taylor(acb_t res, const acb_t x, int reciprocal, slong prec)source

Attempts to compute Γ(x)\Gamma(x), or 1/Γ(x)1/\Gamma(x) if reciprocal is nonzero, with the tabulated Taylor series of 1/Γ(1+x)1/\Gamma(1+x) and argument reduction. Returns 1 on success and 0, without changing res, if xx or prec is outside the supported range.

The method applies when ∣Im⁡x∣|\operatorname{Im} x| is small (at most 4 to 10, depending on the precision), ∣Re⁡x∣|\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.

Cite this page

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 2026-11-02).