Sharp error bounds for turning point expansions

DOI10.7153/jca-2021-18-05zbMath1499.34454arXiv2009.04666OpenAlexW3203718042MaRDI QIDQ5078336

Amparo Gil, T. M. Dunster, Javier Segura

Publication date: 23 May 2022

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.04666

zbMATH Keywords

asymptotic expansionsturning point theoryAiry functionsWKB methods

Mathematics Subject Classification ID

Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) 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)

Uses Software

• DLMF

Cites Work

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• Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals
• Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions
• Asymptotic Approximations and Error Bounds
• Liouville-Green expansions of exponential form, with an application to modified Bessel functions
• Asymptotic solutions of inhomogeneous differential equations having a turning point
• Simplified error bounds for turning point expansions

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