Publication: Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
dc.contributor.author | Ferreira González, Chelo | |
dc.contributor.author | López García, José Luis | |
dc.contributor.author | Pérez Sinusía, Ester | |
dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
dc.date.accessioned | 2018-12-14T12:04:17Z | |
dc.date.available | 2019-09-28T23:00:10Z | |
dc.date.issued | 2018 | |
dc.description | This 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/10.1080/10652469.2018.1525369 | en |
dc.description.abstract | We 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.sponsorship | This research was supported by Ministerio de Economía, Industria y Competitividad, Gobierno de España (MTM2017-83490-P). | en |
dc.embargo.lift | 2019-09-28 | |
dc.embargo.terms | 2019-09-28 | |
dc.format.extent | 14 p. | |
dc.format.mimetype | application/pdf | en |
dc.identifier.doi | 10.1080/10652469.2018.1525369 | |
dc.identifier.issn | 1065-2469 (Print) | |
dc.identifier.issn | 1476-8291 (Electronic) | |
dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/31781 | |
dc.language.iso | eng | en |
dc.publisher | Taylor & Francis | en |
dc.relation.ispartof | Integral Transforms and Special Functions 2018, Vol. 29, No. 12, 942–954 | en |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83490-P/ES/ | en |
dc.relation.publisherversion | https://doi.org/10.1080/10652469.2018.1525369 | |
dc.rights | © 2018 Informa UK Limited, trading as Taylor & Francis Group | en |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
dc.subject | Hypergeometric function | en |
dc.subject | Convergent expansions | en |
dc.subject | Uniform expansions | en |
dc.title | Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions | en |
dc.type | info:eu-repo/semantics/article | |
dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
dspace.entity.type | Publication | |
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