Impacto
Downloads
Downloads per month over past year
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
Preview |
PDF
Creative Commons Attribution. 459kB |
Official URL: http://dx.doi.org/10.1088/2399-6528/aa8540
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 |
---|---|
Additional Information: | © 2017 The Author(s). |
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 |
Origin of downloads
Repository Staff Only: item control page