Nield--Kuznetsov Functions and Laplace Transforms of Parabolic Cylinder Functions

DOI10.1137/21M1401590zbMath1493.33001arXiv2102.11322OpenAlexW3207503686MaRDI QIDQ5158393

T. M. Dunster

Publication date: 22 October 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.11322

zbMATH Keywords

Laplace transformsasymptotic expansionsparabolic cylinder functionsWKB methods

Mathematics Subject Classification ID

Laplace transform (44A10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (3)

Uniform asymptotic expansions for Lommel, Anger‐Weber, and Struve functions ⋮ Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole ⋮ Computation of parabolic cylinder functions having complex argument

Cites Work

• Computing complex Airy functions by numerical quadrature
• On nonoscillating integrals for computing inhomogeneous Airy functions
• Asymptotic solutions of inhomogeneous differential equations having a turning point
• Simplified error bounds for turning point expansions
• Algorithm 822: GIZ, HIZ
• Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations
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