Simplified error bounds for turning point expansions

DOI10.1142/S0219530520500104zbMath1491.34101arXiv1909.13415OpenAlexW3025564959MaRDI QIDQ5153350

Javier Segura, Amparo Gil, T. M. Dunster

Publication date: 29 September 2021

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.13415

zbMATH Keywords

asymptotic expansionsturning point theoryWKB methodsAiry functins

Mathematics Subject Classification ID

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) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Linear ordinary differential equations and systems in the complex domain (34M03) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (6)

Sharp error bounds for turning point expansions ⋮ 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 ⋮ Nield--Kuznetsov Functions and Laplace Transforms of Parabolic Cylinder Functions ⋮ Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations

Uses Software

• Algorithm 838
• DLMF
• Algorithm 644

Cites Work

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• Asymptotic Approximations and Error Bounds
• Algorithm 644
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• Convergent Expansions for Solutions of Linear Ordinary Differential Equations Having a Simple Turning Point, with an Application to Bessel Functions
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• Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments
• Computation of complex Airy functions and their zeros using asymptotics and the differential equation
• Error Bounds for Asymptotic Expansions in Turning-Point Problems

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