acb_hypgeom_gegenbauer_c
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_gegenbauer_c(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec)sourceSets res to the Gegenbauer polynomial (or Gegenbauer function)
C_n^{m}(z) = \frac{(2m)_n}{\Gamma(n+1)}\,
{}_2F_1\left(-n,2m+n,m+\frac{1}{2},\frac{1-z}{2}\right).
For nonnegative integer n this is a polynomial in m and z, also where the hypergeometric series is undefined; it is then evaluated by direct methods.
Cite this page
The FLINT team, “acb_hypgeom_gegenbauer_c (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_gegenbauer_c.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-gegenbauer-c,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_gegenbauer\_c (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_gegenbauer_c.html},
note = {Generated 2026-10-20}
}