FLINT3.7.0-dev
/

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)source

Computes U(a,b,z)U(a,b,z) by rigorous numerical integration of

U(a,b,z)=1Γ(a)∫0∞e−ztta−1(1+t)b−a−1 dt.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≥1a \ge 1 and z>0z > 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 2026-11-02).