Efficient computation of Laguerre polynomials

DOI10.1016/J.CPC.2016.09.002zbMath1378.65066arXiv1609.00829OpenAlexW2516630121MaRDI QIDQ1686930

Amparo Gil, Nico M. Temme, Javier Segura

Publication date: 18 December 2017

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.00829

zbMATH Keywords

computational algorithmasymptotic expansionsLaguerre polynomialsrecurrence relations

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical approximation and evaluation of special functions (33F05)

Related Items (10)

Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions ⋮ Polynomial series expansions and moment approximations for conditional mean risk sharing of insurance losses ⋮ Asymptotic computation of classical orthogonal polynomials ⋮ Fully numerical Laplace transform methods ⋮ High-order asymptotic expansions of Gaussian quadrature rules with classical and generalized weight functions ⋮ Noniterative Computation of Gauss--Jacobi Quadrature ⋮ The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver ⋮ LaguerrePol ⋮ Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation ⋮ \textsf{ORTHOPOLY}: a library for accurate evaluation of series of classical orthogonal polynomials and their derivatives

Uses Software

• DLMF

Cites Work

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• Sharp bounds for the extreme zeros of classical orthogonal polynomials
• A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates
• Asymptotic estimates for Laguerre polynomials
• Uniform Asymptotic Expansions of Laguerre Polynomials
• Uniform Asymptotic Expansions for Whittaker’s Confluent Hypergeometric Functions
• Numerical Methods for Special Functions

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