Smoothing of the Stokes phenomenon using Mellin-Barnes integrals

DOI10.1016/0377-0427(92)90242-PzbMath0772.33015OpenAlexW1997875197MaRDI QIDQ1195411

Richard B. Paris

Publication date: 26 October 1992

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(92)90242-p

zbMATH Keywords

confluent hypergeometric functionsStokes phenomenonparabolic cylinder functionStokes multipliersMellin-Barnes' integrals

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other functions defined by series and integrals (33E20) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (8)

Hyperasymptotics and the Stokes' phenomenon ⋮ Uniform asymptotic expansions of integrals: A selection of problems ⋮ Renormalized asymptotic enumeration of Feynman diagrams ⋮ Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators ⋮ Exponentially-improved asymptotics for the gamma function ⋮ Exponentially small expansions of the Wright function on the Stokes lines ⋮ Critical exponents from the weak-coupling, strong-coupling and large-order parametrization of the hypergeometric \((_{k+1}F_k)\) approximants ⋮ Laplace approximations for hypergeometric functions with matrix argument

Cites Work

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• Exponentially-improved asymptotics for the gamma function
• The special functions and their approximations. Vol. I, II
• Stieltjes transforms and the Stokes phenomenon
• Uniform, Exponentially improved, Asymptotic Expansions for the Generalized Exponential Integral
• Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms
• Smoothing of the Stokes phenomenon for high-order differential equations
• Hyperasymptotics
• Uniform asymptotic smoothing of Stokes’s discontinuities

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