fmpq_poly_gegenbauer_c
Synopsis
#include <flint/fmpq_poly.h>void fmpq_poly_gegenbauer_c(fmpq_poly_t poly, ulong n, const fmpq_t a)sourceSets poly to the Gegenbauer (ultraspherical) polynomial C^{(\alpha)}_n(x) = \frac{(2\alpha)_n}{n!}\,{}_2F_1\left(-n,2\alpha+n; \alpha+\frac12;\frac{1-x}{2}\right), for integer n\ge0 and rational \alpha>0. The coefficients are calculated using a hypergeometric recurrence.
Cite this page
The FLINT team, “fmpq_poly_gegenbauer_c (fmpq_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpq_poly/fmpq_poly_gegenbauer_c.html (generated 2026-10-20).
@misc{flint-doc-fmpq-poly-fmpq-poly-gegenbauer-c,
author = {{The FLINT team}},
title = {{fmpq\_poly\_gegenbauer\_c (fmpq\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpq_poly/fmpq_poly_gegenbauer_c.html},
note = {Generated 2026-10-20}
}