Convergent and asymptotic expansions of the Pearcey integral

DOI10.1016/j.jmaa.2015.04.078zbMath1320.41005OpenAlexW2040101846MaRDI QIDQ2348410

Pedro J. Pagola, José Luis López

Publication date: 12 June 2015

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.04.078

zbMATH Keywords

Green functionsfixed point theoremsasymptotic expansionsthird order differential equationsPearcey integral

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other functions defined by series and integrals (33E20)

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Uses Software

• DLMF

Cites Work

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• Olver's asymptotic method revisited; case I
• Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions
• On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• Asymptotic Expansion of the Pearcey Integral Near the Caustic
• A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: application to Pearcey's integral and its derivatives
• The asymptotic behaviour of Pearcey’s integral for complex variables
• Axial and focal-plane diffraction catastrophe integrals