FLINT3.7.0-dev
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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)source

Sets res to U∗(a,b,z)U^{*}(a,b,z) computed with nn terms of the asymptotic series U∗(a,b,z)∼2F0(a,a−b+1;;−1/z)U^{*}(a,b,z) \sim {}_2F_0(a, a-b+1; ; -1/z), with a rigorous bound for the truncation error. Requires n≥0n \ge 0; n<0n < 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 aa or a−b+1a - b + 1 is a nonpositive integer the series terminates and the result is exact up to rounding for every z≠0z \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 2026-11-02).