An extension of Laplace's method

DOI10.1007/s00365-018-9445-3zbMath1436.41019arXiv1802.03962OpenAlexW3101285344MaRDI QIDQ2309570

Gergő Nemes

Publication date: 1 April 2020

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03962

zbMATH Keywords

asymptotic expansionsLaplace's methodtransition regions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (2)

Uniform asymptotic expansions for Lommel, Anger‐Weber, and Struve functions ⋮ Eisenstein series and an asymptotic for the \(K\)-Bessel function

Uses Software

• DLMF

Cites Work

• An explicit formula for the coefficients in Laplace's method
• The confluent hypergeometric functions \(M(a,b;z)\) and \(U(a,b;z)\) for large \(b\) and \(z\)
• Asymptotics via iterated Mellin-Barnes integrals: Application to the generalised Faxén integral
• Exponentially small expansions of the Wright function on the Stokes lines
• The resurgence properties of the incomplete gamma function, I
• The resurgence properties of the large order asymptotics of the Anger-Weber function I
• Asymptotic Methods for Integrals
• Uniform Asymptotic Expansions of Confluent Hypergeometric Functions
• Why Steepest Descents?
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