acb_hypgeom_u_asymp
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong n, slong prec)sourceSets res to U^{*}(a,b,z) computed with n terms of the asymptotic series U^{*}(a,b,z) \sim {}_2F_0(a, a-b+1; ; -1/z), with a rigorous bound for the truncation error. Requires n \ge 0; n < 0 chooses the number of terms automatically.
The error bound is that of Olver [NIST2012, §13.7], with the case distinction described in Asymptotic expansions. If a or a - b + 1 is a nonpositive integer the series terminates and the result is exact up to rounding for every z \ne 0.
References#
- [NIST2012] National Institute of Standards and Technology, Digital Library of Mathematical Functions (2012), https://dlmf.nist.gov/
Cite this page
The FLINT team, “acb_hypgeom_u_asymp (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_asymp.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-u-asymp,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_u\_asymp (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_asymp.html},
note = {Generated 2026-10-20}
}