Asymptotics of the first Appell functionF1with large parameters II

DOI10.1080/10652469.2013.798658zbMath1282.33022OpenAlexW4256363898MaRDI QIDQ2867927

Pedro J. Pagola, Ester Pérez Sinusía, José Luis López

Publication date: 20 December 2013

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2013.798658

zbMATH Keywords

asymptotic expansionLaplace's methodfirst Appell hypfunction

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Appell, Horn and Lauricella functions (33C65)

Uses Software

• DLMF

Cites Work

• A simplification of Laplace's method: applications to the gamma function and Gauss hypergeometric function
• Large parameter cases of the Gauss hypergeometric function
• Nonlinear ordinary and partial differential equations associated with Appell functions
• NEW PROPERTIES OF THE P. E. APPELL HYPERGEOMETRIC SERIES F₂(α;β, β′;γ, γ′;x, y) TO THE VICINITY OF THE SINGULAR POINT (1, 1) AND NEAR THE BOUNDARY OF ITS DOMAIN OF CONVERGENCE D₂:|x|+|y|<1
• Asymptotic Expansions of Mellin Convolution Integrals
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• The Laplace's and steepest descents methods revisited
• Hypergeometric integrals arising in atomic collisions physics
• The Appell hypergeometric functions and classical separable mechanical systems
• Asymptotic expansions of the Appell’s function 𝐹₁
• Computing the Coefficients in Laplace's Method
• Integration of the Partial Differential Equations for the Hypergeometric Functions F1 and FD of Two and More Variables
• Numerical evaluation of Appell's \(F_1\) hypergeometric function