arb_hypgeom_2f1_integration
Synopsis
#include <flint/arb_hypgeom.h>void arb_hypgeom_2f1_integration(arb_t res, const arb_t a, const arb_t b, const arb_t c, const arb_t z, int regularized, slong prec)sourceComputes {}_2F_1(a,b,c,z) (regularized if regularized is nonzero) by rigorous numerical integration of
{}_2F_1(a,b,c,z) = \frac{\Gamma(c)}{\Gamma(b) \Gamma(c-b)} \int_0^1
t^{b-1} (1-t)^{c-b-1} (1-zt)^{-a} \, dt.
The result is finite only if b \ge 1, c - b \ge 1 and z < 1, possibly after exchanging a and b. acb_hypgeom_2f1 uses it as a fallback for real arguments.
Cite this page
The FLINT team, “arb_hypgeom_2f1_integration (arb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_2f1_integration.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-2f1-integration,
author = {{The FLINT team}},
title = {{arb\_hypgeom\_2f1\_integration (arb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_2f1_integration.html},
note = {Generated 2026-10-20}
}