acb_hypgeom_u_1f1
Synopsis
#include <flint/acb_hypgeom.h>Sets res to U(a,b,z) computed from the convergent series by the connection formula
U(a,b,z) = \frac{\Gamma(1-b)}{\Gamma(a-b+1)} M(a,b,z) +
\frac{\Gamma(b-1)}{\Gamma(a)} z^{1-b} M(a-b+1,2-b,z).
If b is an integer the limit is computed with acb_hypgeom_u_1f1_series; the output is indeterminate if b is inexact and contains an integer.
Cite this page
The FLINT team, “acb_hypgeom_u_1f1 (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_u_1f1.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-u-1f1,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_u\_1f1 (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_u_1f1.html},
note = {Generated 2026-10-20}
}