FLINT3.7.0-dev
/

_arb_poly_gamma_series, arb_poly_gamma_series, _arb_poly_rgamma_series, arb_poly_rgamma_series, _arb_poly_lgamma_series, arb_poly_lgamma_series, _arb_poly_digamma_series, arb_poly_digamma_series

Synopsis#include <flint/arb_poly.h>
void _arb_poly_gamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec)source
void arb_poly_gamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec)source
void _arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec)source
void arb_poly_rgamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec)source
void _arb_poly_lgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec)source
void arb_poly_lgamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec)source
void _arb_poly_digamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec)source
void arb_poly_digamma_series(arb_poly_t res, const arb_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.

These functions compute the Taylor series at the constant term h_0 and compose it with h - h_0 by _arb_poly_compose_series. The Taylor coefficients come from the zeta values \zeta(2), \zeta(3), \ldots when h_0 is a small integer, and otherwise from Stirling's series after shifting the argument by a rising factorial; the Stirling sum is evaluated as a power series by binary splitting (The gamma function).

Guides#

Cite this page

The FLINT team, “_arb_poly_gamma_series, arb_poly_gamma_series, _arb_poly_rgamma_series, arb_poly_rgamma_series, _arb_poly_lgamma_series, arb_poly_lgamma_series, _arb_poly_digamma_series, arb_poly_digamma_series (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_gamma_series.html (generated 2026-10-20).