Efficient computation of Laguerre polynomials

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials L (α) n (z) are presented. The standard threeterm 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 can be obtained using the module LaguerrePol for computing the functions L (α) n (z) in the parameter range z ≥ 0, −1 < α ≤ 5, n ≥ 0.