Dispersive hyperasymptotics and the anharmonic oscillator
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).
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Description/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.
| Item Type: | Article |
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| Related URLs: | |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |
| Item ID: | 29214 |
| Date Deposited: | 11 May 2006 |
| Last Modified: | 02 Mar 2012 12:27 |
| Contributors: | Alvarez, Gabriel (Author) Howls, Christopher J. (Author) Silverstone, Harris J. (Author) |
| Date: | 2002 |
| Status: | Published |
| URI: | http://eprints.soton.ac.uk/id/eprint/29214 |
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