`gr_legendre_p, gr_legendre_q`

Synopsis#include <flint/gr_special.h>

int gr_legendre_p(gr_ptr res, gr_srcptr n, gr_srcptr m, gr_srcptr z, int type, gr_ctx_t ctx)source

int gr_legendre_q(gr_ptr res, gr_srcptr n, gr_srcptr m, gr_srcptr z, int type, gr_ctx_t ctx)source

Set res to the associated Legendre functions of the first and second kind $P_n^m(z)$ and $Q_n^m(z)$ ; type selects the branch cut convention: 0 for Ferrers' functions on $(-1, 1)$ and 1 for the functions on $\mathbb{C} \setminus (-\infty, 1]$ (types 2 and 3 of Mathematica), as in acb_hypgeom_legendre_p.

Cite this page

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

@misc{flint-doc-gr-special-gr-legendre-p,
  author       = {{The FLINT team}},
  title        = {{gr\_legendre\_p, gr\_legendre\_q (gr\_special.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/gr_special/gr_legendre_p.html},
  note         = {Generated 2026-11-02}
}

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