Efficient computation of Laguerre polynomials

Abstract

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L_n^{(\hat{I}\pm )}(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for $n$ large and $\hat{I}\pm$ small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter $\hat{I}\pm$ and the degree $n$ satisfied by the polynomials, we claim that a relative accuracy close or better than $10^{-12}$ can be obtained using the module LaguerrePol for computing the functions $L_n^{(\hat{I}\pm )}(z)$ in the parameter range $z\ge 0$, $-1<\hat{I}\pm \le 5$, $n\ge 0$.

To appear in Computer Physics Communications