On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. I: Real variable

DOI10.1016/j.cam.2003.10.005zbMath1052.41016OpenAlexW2044035340MaRDI QIDQ596153

Richard B. Paris

Publication date: 10 August 2004

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.2003.10.005

zbMATH Keywords

asymptoticshyperasymptoticsHadamard expansionsLaplace-type integrals

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (10)

Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions ⋮ 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 ⋮ On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. II: Complex variable ⋮ Superinterpolation in highly oscillatory quadrature ⋮ Olver's asymptotic method revisited; case I ⋮ The evaluation of Bessel functions via exp-arc integrals ⋮ Uniform asymptotics and zeros of a system of orthogonal polynomials defined via a difference equation ⋮ Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal ⋮ Hadamard expansions for integrals with saddles coalescing with an endpoint

Cites Work

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• Exponentially-improved asymptotics for the gamma function
• Hyperasymptotic solutions of second-order linear differential equations. I
• Infinitely many Stokes smoothings in the gamma function
• Hyperasymptotics for integrals with saddles
• Hyperasymptotics for integrals with finite endpoints
• On the use of Hadamard expansions in hyperasymptotic evaluation. II Complex variables
• On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables
• Hyperasymptotics
• Hyperdeterminants. I

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