Numerical and asymptotic aspects of parabolic cylinder functions

DOI10.1016/S0377-0427(00)00347-2zbMath0966.65023arXivmath/0109188MaRDI QIDQ1587404

Nico M. Temme

Publication date: 20 November 2000

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

Full work available at URL: https://arxiv.org/abs/math/0109188

zbMATH Keywords

algorithmsnumerical testsuniform asymptotic expansionsAiry functionsWeber parabolic cylinder functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

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Uses Software

• Maple
• Mathematica

Cites Work

• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments
• Numerical algorithms for uniform Airy-type asymptotic expansions
• Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders
• UNIFORM ASYMPTOTIC EXPANSIONS OF LAPLACE INTEGRALS
• Laplace type integrals: transformation to standard form and uniform asymptotic expansions
• The Confluent Hypergeometric Function
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