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Hyperasymptotics and the Stokes' phenomenon

Published online by Cambridge University Press:  14 November 2011

A. B. Olde Daalhuis
A. B. Olde Daalhuis
Affiliation:
CWI, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands aod©cwi.nl
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Synopsis

Hyperasymptotic expansions were recently introduced by Berry and Howls, and yield refined information by expanding remainders in asymptotic expansions. In a recent paper of Olde Daalhuis, a method was given for obtaining hyperasymptotic expansions of integrals that represent the confluent hypergeometric U-function. This paper gives an extension of that method to neighbourhoods of the so-called Stokes lines. At each level, the remainder is exponentially small compared with the previous remainders. Two numerical illustrations confirm these exponential improvements.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 4 , 1993 , pp. 731 - 743
Copyright
Copyright © Royal Society of Edinburgh 1993

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