FLINT3.7.0-dev

acb_hypgeom_pfq_bound_factor

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_pfq_bound_factor(mag_t C, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, ulong n)source

Sets C to a factor such that ∣∑k=n∞T(k)∣≤C∣T(n)∣\left|\sum_{k=n}^{\infty} T(k)\right| \le C |T(n)|. The bound is infinite if p>qp > q, if Re⁡(bi+n)>0\operatorname{Re}(b_i + n) > 0 fails for some ii, or if nn is too small for the term ratio to be bounded below 1, even when the series converges. See Convergent series.

Cite this page

The FLINT team, “acb_hypgeom_pfq_bound_factor (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_pfq_bound_factor.html (generated 2026-11-02).