A systematization of the saddle point method. Application to the Airy and Hankel functions

DOI10.1016/j.jmaa.2008.12.032zbMath1163.65013OpenAlexW2015683535MaRDI QIDQ1018193

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

Publication date: 13 May 2009

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.2008.12.032

zbMATH Keywords

numerical examplesAiry functionsaddle point methodHankel functionasymptotic expansions of integralssteepest descent paths

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Other functions defined by series and integrals (33E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical approximation and evaluation of special functions (33F05)

Related Items (13)

The swallowtail integral in the highly oscillatory region III ⋮ New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function ⋮ Asymptotic distribution of the zeros of the Ehrhart polynomial of the cross-polytope ⋮ Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals ⋮ An asymptotic expansion of the hyberbolic umbilic catastrophe integral ⋮ A two-parameter extension of Urbanik’s product convolution semigroup ⋮ An explicit formula for the coefficients of the saddle point method ⋮ Revisiting the saddle-point method of Perron ⋮ The Pearcey integral in the highly oscillatory region ⋮ The asymptotic expansion of the swallowtail integral in the highly oscillatory region ⋮ The swallowtail integral in the highly oscillatory region. II ⋮ A Systematic “Saddle Point Near a Pole” Asymptotic Method with Application to the Gauss Hypergeometric Function ⋮ Asymptotic behaviour of the Urbanik semigroup

Cites Work

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• Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank 1
• The Laplace's and steepest descents methods revisited
• Explicit Series Formulae for the Evaluation of Integrals by the Method of Steepest Descents
• Hyperasymptotics for integrals with saddles
• Why Steepest Descents?

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