Dispersive hyperasymptotics and the anharmonic oscillator
نویسندگان
چکیده
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. PACS numbers: 03.65.Sq, 02.30.Gp, 02.60.−x
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