FLINT3.7.0-dev
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_fmpq_poly_gegenbauer_c

Synopsis#include <flint/fmpq_poly.h>
void _fmpq_poly_gegenbauer_c(fmpz * coeffs, fmpz_t den, ulong n, const fmpq_t a)source

Sets coeffs to the coefficient array of the Gegenbauer (ultraspherical) polynomial Cn(α)(x)=(2α)nn! 2F1(−n,2α+n;α+12;1−x2)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≥0n\ge0 and rational α>0\alpha>0. Sets den to the overall denominator. 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 2026-11-02).