Efficient computation of Laguerre polynomials
datasetposted on 18.07.2019, 12:57 by Amparo Gil, Javier Segura, Nico M. Temme
An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials L_n^(α)(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_n^(α)(z) in the parameter range z≥0, −1<α≤5, n≥0.