Efficient computation of Laguerre polynomials
Provides a high-precision computational tool for scientists and engineers who need to evaluate Laguerre polynomials efficiently.
The paper presents an efficient algorithm and Fortran 90 module for computing Laguerre polynomials, achieving relative accuracy close to or better than 10^{-12} for a wide parameter range.
An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L^{(α)}_n(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for $n$ large and $α$ small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter $α$ 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 $L^{(α)}_n(z)$ in the parameter range $z \ge 0$, $-1 < α\le 5$, $n \ge 0$.