Convergent expansions of the confluent hypergeometric functions in terms of elementary functions
| dc.contributor.author | Bujanda Cirauqui, Blanca | |
| dc.contributor.author | López García, José Luis | |
| dc.contributor.author | Pagola Martínez, Pedro Jesús | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.funder | Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa | es |
| dc.date.accessioned | 2018-12-14T12:04:16Z | |
| dc.date.available | 2018-12-14T12:04:16Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | We consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); one of them in terms of incomplete gamma functions γ(a, z) and another one in terms of rational functions of ez and z. We also derive a convergent expansion of U(a, b; z) in terms of incomplete gamma functions γ(a, z) and Γ(a, z). The expansions of M(a, b; z) hold uniformly in either Rz ≥ 0 or Rz ≤ 0; the expansion of U(a, b; z) holds uniformly in Rz > 0. The accuracy of the approximations is illustrated by means of some numerical experiments. | en |
| dc.description.sponsorship | This research was supported by the Spanish Ministry of Economía y Competitividad, projects MTM2014-53178-P and TEC2013-45585-C2-1-R. The Universidad Pública de Navarra is acknowledged for its financial support. | en |
| dc.format.extent | 18 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1090/mcom/3389 | |
| dc.identifier.issn | 0025-5718 (Print) | |
| dc.identifier.issn | 1088-6842 (Electronic) | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/31779 | |
| dc.language.iso | eng | en |
| dc.publisher | American Mathematical Society | en |
| dc.relation.ispartof | Mathematics of Computation, Volume 88, Number 318, July 2019, Pages 1773–1789 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-53178-P/ES/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//TEC2013-45585-C2-1-R/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1090/mcom/3389 | |
| dc.rights | © Copyright 2018 American Mathematical Society | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Confluent hypergeometric functions | en |
| dc.title | Convergent expansions of the confluent hypergeometric functions in terms of elementary functions | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
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