The Pearcey integral in the highly oscillatory region II

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dc.contributor.authorFerreira González, Chelo
dc.contributor.authorLópez García, José Luis
dc.contributor.authorPérez Sinusía, Ester
dc.contributor.departmentEstadística, Informática y Matemáticases_ES
dc.contributor.departmentEstatistika, Informatika eta Matematikaeu
dc.contributor.departmentInstitute for Advanced Materials and Mathematics - INAMAT2en
dc.date.accessioned2025-07-02T17:45:12Z
dc.date.available2025-07-02T17:45:12Z
dc.date.issued2025-08-01
dc.date.updated2025-07-02T17:32:47Z
dc.description.abstractWe consider the Pearcey integral P(x, y) for large values of |x| and bounded values of |y|. The standard saddle point analysis is difficult to apply because the Pearcey integral is highly oscillating in this region. To overcome this problem we use the modified saddle point method introduced in López et al. (2009). A complete asymptotic analysis is possible with this method, and we derive a complete asymptotic expansion of P(x, y) for large |x|, accompanied by the exact location of the Stokes lines. There are two Stokes lines that divide the complex x−plane in two different sectors in which P(x, y) behaves differently when |x| is large. The asymptotic approximation is the sum of two asymptotic series whose terms are elementary functions of x and y. Both of them are of Poincaré type; one of them is given in terms of inverse powers of x; the other one in terms of inverse powers of x 1/2 , and it is multiplied by an exponential factor that behaves differently in the two mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation.en
dc.description.sponsorshipThis research was supported by the Spanish Ministerio de Ciencia, Innovación y Universidades, project PID2022-136441NB-I00.
dc.format.mimetypeapplication/pdf
dc.identifier.citationFerreira, C., López, J. L., Pérez Sinusía, E. (2025) The Pearcey integral in the highly oscillatory region II. Journal of Approximation Theory, 309, 1-13. https://doi.org/10.1016/j.jat.2025.106150
dc.identifier.doi10.1016/j.jat.2025.106150
dc.identifier.issn0021-9045
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/54377
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofJournal of Approximation Theory 309, 2025, 106150
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136441NB-I00/ES/
dc.relation.publisherversionhttps://doi.org/10.1016/j.jat.2025.106150
dc.rights© 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license.
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectPearcey integralen
dc.subjectAsymptotic expansionsen
dc.subjectSimplified saddle point methoden
dc.titleThe Pearcey integral in the highly oscillatory region IIen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dspace.entity.typePublication
relation.isAuthorOfPublication8b28fd50-66f4-431e-a219-43d8c02bb077
relation.isAuthorOfPublicatione6cd33c5-6d5e-455c-b8da-32a9702e16c8
relation.isAuthorOfPublication93f891c7-529d-4972-8759-9d943c60949c
relation.isAuthorOfPublication.latestForDiscoverye6cd33c5-6d5e-455c-b8da-32a9702e16c8

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