acb_hypgeom_pfq_direct
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec)sourceSets res to
{}_pf_{q}(z) = \sum_{k=0}^{\infty} T(k) = \sum_{k=0}^{n-1} T(k) +
\varepsilon,
computed directly from the series with acb_hypgeom_pfq_sum and a rigorous bound for the truncation error \varepsilon from acb_hypgeom_pfq_bound_factor. If n < 0, the number of terms is chosen with acb_hypgeom_pfq_choose_n. If T(n) is exactly zero (a terminating series), no error is added. For real input the error is added to the real part only.
Cite this page
The FLINT team, “acb_hypgeom_pfq_direct (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_direct.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-pfq-direct,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_pfq\_direct (acb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_pfq_direct.html},
note = {Generated 2026-10-20}
}