FLINT3.7.0-dev
/

acb_hypgeom_gamma_stirling_sum_horner, acb_hypgeom_gamma_stirling_sum_improved

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_gamma_stirling_sum_horner(acb_t s, const acb_t z, slong N, slong prec)source
void acb_hypgeom_gamma_stirling_sum_improved(acb_t s, const acb_t z, slong N, slong K, slong prec)source

Sets s to ∑n=1N−1B2n/(2n(2n−1)z2n−1)\sum_{n=1}^{N-1} B_{2n} / (2n(2n-1) z^{2n-1}), the sum in the Stirling series truncated before the term of index NN, using Horner's scheme or the improved algorithm with splitting parameter KK (0 to choose it), as arb_hypgeom_gamma_stirling_sum_horner and arb_hypgeom_gamma_stirling_sum_improved do for real zz. No bound for the truncation error is added.

Cite this page

The FLINT team, “acb_hypgeom_gamma_stirling_sum_horner, acb_hypgeom_gamma_stirling_sum_improved (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_stirling_sum_horner.html (generated 2026-11-02).