Efficient computation of Laguerre polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2017Embargo end date: 01 Jan 2016 Netherlands, Spain English Publisher:Elsevier BVJournal:Computer Physics Communications, volume 210, pages 124-131 (issn: 0010-4655,

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Authors: A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico);

doi: 10.1016/j.cpc.2016.09.002 , 10.48550/arxiv.1609.00829

arXiv: 1609.00829

handle: 10902/11339

Efficient computation of Laguerre polynomials

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Abstract

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 $z \ge 0$, $-1 < α\le 5$, $n \ge 0$.

To appear in Computer Physics Communications

Countries

Netherlands, Spain

Related Organizations

San Diego State University
United States
Centrum Wiskunde & Informatica
Netherlands
University of Cantabria
Spain
Dutch Research Council
Netherlands

Keywords

FOS: Computer and information sciences, Computational algorithm, recurrence relations, Recurrence relations, Numerical Analysis (math.NA), asymptotic expansions, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Asymptotic expansions, Computation of special functions and constants, construction of tables, computational algorithm, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Laguerre polynomials, Computer Science - Mathematical Software, Bessel and Airy functions, cylinder functions, ${}_0F_1$, Mathematics - Numerical Analysis, Numerical approximation and evaluation of special functions, Mathematical Software (cs.MS)

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