Efficient computation of Laguerre polynomials

Abstract

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials View the MathML source are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for n large and a small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter a 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 View the MathML source in the parameter range z=0, -1<a=5, n=0. Program summary Program Title: Module LaguerrePol Program Files doi:http://dx.doi.org/10.17632/3jkk659cn8.1 Licensing provisions: CC by 4.0 Programming language: Fortran 90 Nature of problem: Laguerre polynomials View the MathML source appear in a vast number of applications in physics, such as quantum mechanics, plasma physics, etc. Solution method: The algorithm uses asymptotic expansions or recurrence relations for computing the function values depending on the range of parameters. Restrictions: The admissible input parameter ranges for computing the Laguerre View the MathML source are z=0, -1<a=5, n=0.