Analytic formulas for the evaluation of the Pearcey integral

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Date
2017Version
Acceso abierto / Sarbide irekia
Type
Artículo / Artikulua
Version
Versión aceptada / Onetsi den bertsioa
Impact
|
10.1090/mcom/3164
Abstract
We can find in the literature several convergent and/or asymptotic
expansions of the Pearcey integral P(x, y) in different regions of the complex
variables x and y, but they do not cover the whole complex x and y planes.
The purpose of this paper is to complete this analysis giving new convergent
and/or asymptotic expansions that, together with the known ones, cover the
evaluation of the Pea ...
[++]
We can find in the literature several convergent and/or asymptotic
expansions of the Pearcey integral P(x, y) in different regions of the complex
variables x and y, but they do not cover the whole complex x and y planes.
The purpose of this paper is to complete this analysis giving new convergent
and/or asymptotic expansions that, together with the known ones, cover the
evaluation of the Pearcey integral in a large region of the complex x and y
planes. The accuracy of the approximations derived in this paper is illustrated
with some numerical experiments. Moreover, the expansions derived here are
simpler compared with other known expansions, as they are derived from a
simple manipulation of the integral definition of P(x, y). [--]
Subject
Pearcey integral,
Convergent and asymptotic expansions,
Watson lemma
Publisher
American Mathematical Society
Published in
Mathematics of Computation, 86 (2017), 2399-2407
Departament
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Publisher version
Sponsorship
This research was supported by the Spanish Ministry of “Economía y Competitividad”,
project MTM2014-52859-P. The Universidad Pública de Navarra is
acknowledged for its financial support.