`acb_hypgeom_legendre_p_uiui_rec`

Synopsis#include <flint/acb_hypgeom.h>

void acb_hypgeom_legendre_p_uiui_rec(acb_t res, ulong n, ulong m, const acb_t z, slong prec)source

For nonnegative integers $n$ and $m$ , sets res to $(1-z^2)^{-m/2} P_n^m(z)$ , which is a polynomial in $z$ , computed with the three-term recurrence in the degree starting from $P_m^m$ . The result is zero for $m > n$ , and indeterminate if $(n - m)/4 > \mathit{prec}$ , where the recurrence would lose all accuracy.

Cite this page

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

@misc{flint-doc-acb-hypgeom-acb-hypgeom-legendre-p-uiui-rec,
  author       = {{The FLINT team}},
  title        = {{acb\_hypgeom\_legendre\_p\_uiui\_rec (acb\_hypgeom.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_legendre_p_uiui_rec.html},
  note         = {Generated 2026-11-02}
}

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