FLINT3.7.0-dev
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_acb_poly_gamma_series, acb_poly_gamma_series, _acb_poly_rgamma_series, acb_poly_rgamma_series, _acb_poly_lgamma_series, acb_poly_lgamma_series, _acb_poly_digamma_series, acb_poly_digamma_series

Synopsis#include <flint/acb_poly.h>
void _acb_poly_gamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec)source
void acb_poly_gamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec)source
void _acb_poly_rgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec)source
void acb_poly_rgamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec)source
void _acb_poly_lgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec)source
void acb_poly_lgamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec)source
void _acb_poly_digamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec)source
void acb_poly_digamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec)source

Set res to \Gamma(h), 1/\Gamma(h), \log \Gamma(h) or \psi(h) truncated to length n. The underscore versions allow aliasing.

If all coefficients of h are real, the corresponding arb_poly function is used. Otherwise the Taylor series at the constant term is computed from Stirling's series after shifting the argument by a rising factorial (and using the reflection formula in the left half-plane), with the parameters of acb_hypgeom_gamma_stirling_choose_param, and composed with h - h_0 (The gamma function). acb_poly_lgamma_series gives the principal branch of the log-gamma function, continuous away from the negative real axis.

Cite this page

The FLINT team, “_acb_poly_gamma_series, acb_poly_gamma_series, _acb_poly_rgamma_series, acb_poly_rgamma_series, _acb_poly_lgamma_series, acb_poly_lgamma_series, _acb_poly_digamma_series, acb_poly_digamma_series (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_gamma_series.html (generated 2026-10-20).