acb_hypgeom_laguerre_l
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_laguerre_l(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec)sourceSets res to the Laguerre polynomial (or Laguerre function)
L_n^{m}(z) = \frac{(m+1)_n}{\Gamma(n+1)}\, {}_1F_1\left(-n,m+1,z\right).
For nonnegative integer n this is a polynomial in m and z, also where the hypergeometric series is undefined; it is then evaluated by direct methods.
There are at least two incompatible extensions to negative integer n: for m = 0 one can define L_{-n}^0(z) = e^z L_{n-1}^0(-z), or one can use the recurrence L_{n-1}^m(z) + L_n^{m-1}(z) = L_n^m(z). This case is left undefined: the result is indeterminate.
Cite this page
The FLINT team, “acb_hypgeom_laguerre_l (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_laguerre_l.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-laguerre-l,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_laguerre\_l (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_laguerre_l.html},
note = {Generated 2026-10-20}
}