FLINT3.7.0-dev
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fmpq_poly_legendre_p

Synopsis#include <flint/fmpq_poly.h>
void fmpq_poly_legendre_p(fmpq_poly_t poly, ulong n)source

Sets poly to the Legendre polynomial Pn(x)P_n(x), defined by (n+1)Pn+1(x)=(2n+1)xPn(x)−nPn−1(x)(n+1) P_{n+1}(x) = (2n+1) x P_n(x) - n P_{n-1}(x), for n≥0n\ge0. The coefficients are calculated using a hypergeometric recurrence in integer arithmetic. The denominator is given by gcd⁡(n!,2n)=2⌊n/2⌋+⌊n/4⌋+….\gcd(n!,2^n) = 2^{\lfloor n/2 \rfloor + \lfloor n/4 \rfloor + \ldots}. See fmpz_poly for the shifted Legendre polynomials.

Cite this page

The FLINT team, “fmpq_poly_legendre_p (fmpq_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpq_poly/fmpq_poly_legendre_p.html (generated 2026-11-02).