arb_hypgeom_u_integration
Synopsis
#include <flint/arb_hypgeom.h>void arb_hypgeom_u_integration(arb_t res, const arb_t a, const arb_t b, const arb_t z, slong prec)sourceComputes U(a,b,z) by rigorous numerical integration of
U(a,b,z) = \frac{1}{\Gamma(a)} \int_0^{\infty} e^{-zt} t^{a-1}
(1+t)^{b-a-1} \, dt.
The result is finite only if a \ge 1 and z > 0. acb_hypgeom_u uses it as a fallback for real arguments in the same way as arb_hypgeom_1f1_integration.
Cite this page
The FLINT team, “arb_hypgeom_u_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_u_integration.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-u-integration,
author = {{The FLINT team}},
title = {{arb\_hypgeom\_u\_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_u_integration.html},
note = {Generated 2026-10-20}
}