acb_hypgeom_spherical_y
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_spherical_y(acb_t res, slong n, slong m, const acb_t theta, const acb_t phi, slong prec)sourceSets res to the spherical harmonic of degree n and order m at latitude angle \theta and longitude angle \phi, normalized so that
Y_n^m(\theta, \phi) = \sqrt{\frac{2n+1}{4\pi} \frac{(n-m)!}{(n+m)!}}\,
e^{im\phi} P_n^m(\cos(\theta)).
The definition is extended to negative m and n by symmetry. The function is a polynomial in \cos\theta and \sin\theta and is evaluated with acb_hypgeom_legendre_p_uiui_rec.
Cite this page
The FLINT team, “acb_hypgeom_spherical_y (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_spherical_y.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-spherical-y,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_spherical\_y (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_spherical_y.html},
note = {Generated 2026-10-20}
}