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 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 to 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≥0 , −1<α≤5 , n≥0 .