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A new method to sum divergent power series: educated match

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Alvarez Galindo, Gabriel and Silverstone, Harris J. (2017) A new method to sum divergent power series: educated match. Journal of physics communications, 1 (2). ISSN 2399-6528

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Official URL: http://dx.doi.org/10.1088/2399-6528/aa8540


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Abstract

We present a method to sum Borel- and Gevrey-summable asymptotic series by matching the series to be summed with a linear combination of asymptotic series of known functions that themselves are scaled versions of a single, appropriate, but otherwise unrestricted, function Phi. Both the scaling and linear coefficients are calculated from Pade approximants of a series transformed from the original series by Phi. We discuss in particular the case that Phi is (essentially) a confluent hypergeometric function, which includes as special cases the standard Borel-Pade and Borel-Leroy-Pade methods. A particular advantage is the mechanism to build knowledge about the summed function into the approximants, extending their accuracy and range even when only a few coefficients are available. Several examples from field theory and Rayleigh-Schrodinger perturbation theory illustrate the method.


Item Type:Article
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© 2017 The Author(s).
We wish to acknowledge the support of the Spanish Ministerio de Economía y Competitividad under Project No. FIS2015-63966-P and of the Department of hemistry of the Johns Hopkins University.

Uncontrolled Keywords:Anharmonic-Oscillator; 3 Dimensions; Model; Summability
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:49128
Deposited On:17 Sep 2018 14:50
Last Modified:10 Dec 2018 15:09

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