arb_hypgeom_legendre_p, arb_hypgeom_legendre_q
Synopsis
#include <flint/arb_hypgeom.h>void arb_hypgeom_legendre_p(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec)sourcevoid arb_hypgeom_legendre_q(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec)sourceSets res to the associated Legendre function of the first kind P_n^m(z) or of the second kind Q_n^m(z), with the branch cut convention selected by type (0 or 1) as described for acb_hypgeom_legendre_p and acb_hypgeom_legendre_q. For m = 0 and a nonnegative integer n < 2^{\mathtt{FLINT\_BITS} - 1}, arb_hypgeom_legendre_p calls arb_hypgeom_legendre_p_ui; otherwise both functions wrap the complex versions.
Cite this page
The FLINT team, “arb_hypgeom_legendre_p, arb_hypgeom_legendre_q (arb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_legendre_p.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-legendre-p,
author = {{The FLINT team}},
title = {{arb\_hypgeom\_legendre\_p, arb\_hypgeom\_legendre\_q (arb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_legendre_p.html},
note = {Generated 2026-10-20}
}