`acb_hypgeom_u_1f1`

Synopsis#include <flint/acb_hypgeom.h>

void acb_hypgeom_u_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec)source

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 2026-11-02).

@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 2026-11-02}
}

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