Uniform, Exponentially improved, Asymptotic Expansions for the Generalized Exponential Integral

DOI10.1137/0522094zbMath0743.41025OpenAlexW4241159483MaRDI QIDQ3982752

F. W. J. Olver

Publication date: 26 June 1992

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0522094

zbMATH Keywords

Stokes phenomenonexponential improvementPoincaré expansions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other special functions (33E99)

Related Items (18)

The Resurgence Properties of the Incomplete Gamma Function II ⋮ Hyperasymptotics and the Stokes' phenomenon ⋮ Error analysis in a uniform asymptotic expansion for the generalised exponential integral ⋮ Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions ⋮ Uniform asymptotic expansions of integrals: A selection of problems ⋮ The resurgence properties of the Hankel and Bessel functions of nearly equal order and argument ⋮ A stable recurrence for the incomplete gamma function with imaginary second argument ⋮ Analytical properties of generalized Gaussian distributions ⋮ Smoothing of the Stokes phenomenon using Mellin-Barnes integrals ⋮ In memoriam Frank W. J. Olver (1924–2013) ⋮ The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions ⋮ Exponentially small expansions of the Wright function on the Stokes lines ⋮ Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal ⋮ The resurgence properties of the large order asymptotics of the Anger-Weber function I ⋮ The resurgence properties of the large order asymptotics of the Anger-Weber function II ⋮ Asymptotics of the Mittag-Leffler function \(E_a(z)\) on the negative real axis when \(a \rightarrow 1\) ⋮ Exponential asymptotics of the Voigt functions ⋮ Dingle’s final main rule, Berry’s transition, and Howls’ conjecture ^*

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