Asymptotics and bounds for the zeros of Laguerre polynomials: A survey

DOI10.1016/S0377-0427(01)00549-0zbMath1008.65011MaRDI QIDQ1612353

Luigi Gatteschi

Publication date: 22 August 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesLaguerre polynomialHermite polynomialasymptotics of zerosBessel functionAiry functionWhittaker functionLiouville-Green transformuniform asymptotic approximationbounds of zeros

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 (19)

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Cites Work

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• Sugli zeri delle funzioni di cui si conosce una rappresentazione asintotica
• Sul comportamente asintotico dell'n -esimo polinomio di Laguerre nell'intorno dell'ascissa 4n
• Sul comportamento asintotico dei polinomi di Laguerre
• 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
• Bound on the Extreme Zeros of Orthogonal Polynomials
• A new asymptotic form for the Laguerre polynomials
• New asymptotics for the zeros of Whittaker's functions

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