Efficient computation of Laguerre polynomials

Published: 29-09-2016| Version 1 | DOI: 10.17632/3jkk659cn8.1
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.