@article{10902/11339,
year = {2017},
month = {1},
url = {http://hdl.handle.net/10902/11339},
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.},
organization = {The authors acknowledge financial support from Ministerio de Ciencia e Innovación, projects MTM2012-34787, MTM2015-67142-P},
publisher = {Elsevier},
publisher = {Computer Physics Communications Volume 210, January 2017, Pages 124–131},
title = {Efficient computation of Laguerre polynomials},
author = {Gil Gómez, Amparo and Segura Sala, José Javier and Temme, Nicolaas Maria},
}