Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

DOI10.1016/J.CAM.2005.01.038zbMath1086.65012OpenAlexW2051448251MaRDI QIDQ818273

N. E. Zubov

Publication date: 24 March 2006

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.01.038

zbMATH Keywords

numerical resultshyperasymptoticsHadamard expansionsPearcey integralcaustic curveStokes set

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Other functions defined by series and integrals (33E20) Numerical approximation and evaluation of special functions (33F05)

Related Items (9)

On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. IV: Poles ⋮ On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. III: Clusters of saddle points ⋮ The swallowtail integral in the highly oscillatory region III ⋮ Analytic formulas for the evaluation of the Pearcey integral ⋮ ASYMPTOTIC AND CONVERGENT EXPANSIONS FOR SOLUTIONS OF THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH A LARGE PARAMETER ⋮ The asymptotic expansion of the swallowtail integral in the highly oscillatory region ⋮ High-precision evaluation of the Bessel functions via Hadamard series ⋮ The swallowtail integral in the highly oscillatory region. II ⋮ Convergent and asymptotic expansions of the Pearcey integral

Cites Work

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• On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. I: Real variable
• On the zeros of the Pearcey integral
• Exactification of the method of steepest descents: the Bessel functions of large order and argument
• The Stokes set of the cusp diffraction catastrophe
• 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
• Hyperasymptotics for integrals with saddles

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