Asymptotic estimates for Laguerre polynomials

DOI10.1007/BF00946078zbMath0688.33007OpenAlexW2164646192MaRDI QIDQ1263711

Nico M. Temme

Publication date: 1990

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00946078

zbMATH Keywords

Laguerre polynomial

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)

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Expansions in series of varying Laguerre polynomials and some applications to molecular potentials ⋮ Large parameter cases of the Gauss hypergeometric function ⋮ Asymptotics of Plancherel-type random partitions ⋮ Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions ⋮ Spectral expansions of non-self-adjoint generalized Laguerre semigroups ⋮ A new asymptotic form for the Laguerre polynomials ⋮ Efficient computation of Laguerre polynomials ⋮ Transformation to canonical form for uniform asymptotic expansions ⋮ Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation ⋮ Strong asymptotics for Laguerre polynomials with varying weights ⋮ On the distribution of the largest eigenvalue in principal components analysis ⋮ Asymptotics for Laguerre polynomials with large order and parameters ⋮ A NUMERICAL EVALUATION OF VACUUM POLARIZATION TENSOR IN CONSTANT EXTERNAL MAGNETIC FIELDS ⋮ Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters ⋮ Asymptotics and bounds for the zeros of Laguerre polynomials: A survey

Cites Work

• Uniform Asymptotic Expansions of Laguerre Polynomials
• Uniform Asymptotic Expansions for Whittaker’s Confluent Hypergeometric Functions
• Whittaker functions with both parameters large: uniform approximations in terms of parabolic cylinder functions
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