Publication:
Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions

dc.contributor.authorFerreira González, Chelo
dc.contributor.authorLópez García, José Luis
dc.contributor.authorPérez Sinusía, Ester
dc.contributor.departmentMatematika eta Informatika Ingeniaritzaeu
dc.contributor.departmentInstitute for Advanced Materials and Mathematics - INAMAT2en
dc.contributor.departmentIngeniería Matemática e Informáticaes_ES
dc.date.accessioned2018-12-14T12:04:17Z
dc.date.available2019-09-28T23:00:10Z
dc.date.issued2018
dc.descriptionThis is an accepted manuscript of an article published by Taylor & Francis in Integral Transforms and Special Functions on 2018-09-28, available online: https://doi.org/10.1080/10652469.2018.1525369en
dc.description.abstractWe consider the hypergeometric function 2F1(a, b; c; z) for z ∈ C \ [1,∞). For Ra ≥ 0, we derive a convergent expansion of 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly valid for z in any compact in C \ [1,∞). When a ∈ N, the expansion also contains a logarithmic term of the form log(1 − z). For Ra ≤ 0, we derive a convergent expansion of (1 − z)a 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly valid for z in any compact in C \ [1,∞) in the exterior of the circle |z − 1| = r for arbitrary r > 0. The expansions are accompanied by realistic error bounds. Some numerical experiments show the accuracy of the approximation.en
dc.description.sponsorshipThis research was supported by Ministerio de Economía, Industria y Competitividad, Gobierno de España (MTM2017-83490-P).en
dc.embargo.lift2019-09-28
dc.embargo.terms2019-09-28
dc.format.extent14 p.
dc.format.mimetypeapplication/pdfen
dc.identifier.doi10.1080/10652469.2018.1525369
dc.identifier.issn1065-2469 (Print)
dc.identifier.issn1476-8291 (Electronic)
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/31781
dc.language.isoengen
dc.publisherTaylor & Francisen
dc.relation.ispartofIntegral Transforms and Special Functions 2018, Vol. 29, No. 12, 942–954en
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83490-P/ES/en
dc.relation.publisherversionhttps://doi.org/10.1080/10652469.2018.1525369
dc.rights© 2018 Informa UK Limited, trading as Taylor & Francis Groupen
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectHypergeometric functionen
dc.subjectConvergent expansionsen
dc.subjectUniform expansionsen
dc.titleUniform convergent expansions of the Gauss hypergeometric function in terms of elementary functionsen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersionen
dc.type.versionVersión aceptada / Onetsi den bertsioaes
dspace.entity.typePublication
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relation.isAuthorOfPublicatione6cd33c5-6d5e-455c-b8da-32a9702e16c8
relation.isAuthorOfPublication93f891c7-529d-4972-8759-9d943c60949c
relation.isAuthorOfPublication.latestForDiscovery8b28fd50-66f4-431e-a219-43d8c02bb077

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