`acb_hypgeom_u_1f1_series`

Synopsis#include <flint/acb_hypgeom.h>

void acb_hypgeom_u_1f1_series(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t z, slong len, slong prec)

source

Sets res to $U(a,b,z)$ as a power series truncated to length len, for power series $a, b, z \in \mathbb{C}[[x]]$ , using the connection formula with two ${}_1F_1$ series. If the constant term of $b$ is an integer, one extra derivative is computed and the removable singularity is divided out; it is then assumed that the coefficient of $x$ in $b$ is nonzero. The output is indeterminate if the constant term of $b$ is inexact and contains an integer.

Cite this page

The FLINT team, “acb_hypgeom_u_1f1_series (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_series.html (generated 2026-11-02).

@misc{flint-doc-acb-hypgeom-acb-hypgeom-u-1f1-series,
  author       = {{The FLINT team}},
  title        = {{acb\_hypgeom\_u\_1f1\_series (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_series.html},
  note         = {Generated 2026-11-02}
}

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