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Analytic formulas for the evaluation of the Pearcey integral


Authors: José L. López and Pedro J. Pagola
Journal: Math. Comp. 86 (2017), 2399-2407
MSC (2010): Primary 33E20, 41A60
DOI: https://doi.org/10.1090/mcom/3164
Published electronically: September 27, 2016
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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 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)$.


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Additional Information

José L. López
Affiliation: Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Las Encinas 31006, Pamplona, Spain
Email: jl.lopez@unavarra.es

Pedro J. Pagola
Affiliation: Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Las Encinas 31006, Pamplona, Spain
Email: pedro.pagola@unavarra.es

DOI: https://doi.org/10.1090/mcom/3164
Keywords: Pearcey integral, convergent and asymptotic expansions, Watson lemma
Received by editor(s): November 9, 2015
Received by editor(s) in revised form: February 23, 2016
Published electronically: September 27, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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