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Dispersive hyperasymptotics and the anharmonic oscillator

Dispersive hyperasymptotics and the anharmonic oscillator
Dispersive hyperasymptotics and the anharmonic oscillator
Hyperasymptotic summation of steepest-descent asymptotic expansions of integrals is extended to functions that satisfy a dispersion relation. We apply the method to energy eigenvalues of the anharmonic oscillator, for which there is no known integral representation, but for which there is a dispersion relation. Hyperasymptotic summation exploits the rich analytic structure underlying the asymptotics and is a practical alternative to Borel summation of the Rayleigh–Schrödinger perturbation series.
0305-4470
4017-4042
Alvarez, Gabriel
5227cb90-72f6-4b7d-99ab-a3a7299f8ab2
Howls, Christopher J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Silverstone, Harris J.
918b6a1a-9f33-4a7a-adb9-8ba64725f343
Alvarez, Gabriel
5227cb90-72f6-4b7d-99ab-a3a7299f8ab2
Howls, Christopher J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Silverstone, Harris J.
918b6a1a-9f33-4a7a-adb9-8ba64725f343

Alvarez, Gabriel, Howls, Christopher J. and Silverstone, Harris J. (2002) Dispersive hyperasymptotics and the anharmonic oscillator. Journal of Physics A: Mathematical and General, 35 (18), 4017-4042. (doi:10.1088/0305-4470/35/18/303).

Record type: Article

Abstract

Hyperasymptotic summation of steepest-descent asymptotic expansions of integrals is extended to functions that satisfy a dispersion relation. We apply the method to energy eigenvalues of the anharmonic oscillator, for which there is no known integral representation, but for which there is a dispersion relation. Hyperasymptotic summation exploits the rich analytic structure underlying the asymptotics and is a practical alternative to Borel summation of the Rayleigh–Schrödinger perturbation series.

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Published date: 2002
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29214
URI: http://eprints.soton.ac.uk/id/eprint/29214
ISSN: 0305-4470
PURE UUID: 67976acc-60cc-4634-bccd-96c7f4d54a04
ORCID for Christopher J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

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Date deposited: 11 May 2006
Last modified: 20 Jul 2019 01:08

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Contributors

Author: Gabriel Alvarez
Author: Harris J. Silverstone

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