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    Analytic formulas for the evaluation of the Pearcey integral

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    Date
    2017
    Author
    López García, José Luis Upna Orcid
    Pagola Martínez, Pedro Jesús Upna
    Version
    Acceso abierto / Sarbide irekia
    Type
    Artículo / Artikulua
    Version
    Versión aceptada / Onetsi den bertsioa
    Project Identifier
    ES/1PE/MTM2014-52859 
    Impact
     
     
     
    10.1090/mcom/3164
     
     
     
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    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
    https://doi.org/10.1090/mcom/3164
    URI
    https://hdl.handle.net/2454/31773
    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.
    Appears in Collections
    • Artículos de revista DIMI - MIIS Aldizkari artikuluak [58]
    • Artículos de revista - Aldizkari artikuluak [4205]
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