|
Título:
|
A new method to sum divergent power series: educated match
|
|
Autores:
|
Álvarez Galindo, Gabriel ;
Silverstone, Harris J.
|
|
Tipo de documento:
|
texto impreso
|
|
Editorial:
|
IOP publishing ltd, 2017-09
|
|
Dimensiones:
|
application/pdf
|
|
Nota general:
|
cc_by
info:eu-repo/semantics/openAccess
|
|
Idiomas:
|
|
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Física: Física-Modelos matemáticos
,
Materia = Ciencias: Física: Física matemática
,
Tipo = Artículo
|
|
Resumen:
|
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.
|
|
En línea:
|
https://eprints.ucm.es/49128/1/alvarez16libre%2BCC.pdf
|
