Efficient computation of Laguerre polynomials

09/03/2016

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by   A. Gil, et al.

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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 > 0, -1 < α< 5, n > 0.