Uniform representation of the incomplete beta 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 | 2018-12-14T12:04:17Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | We consider the incomplete beta function Bz(a, b) in the maximum domain of analyticity of its three variables: a, b, z ∈ C, −a /∈ N, z /∈ [1, ∞). For <b ≤ 1 we derive a convergent expansion of z−aBz(a, b) in terms of the function (1 − z) b and of rational functions of z that is uniformly valid for z in any compact set in C \ [1, ∞). When −b ∈ N ∪ {0}, the expansion also contains a logarithmic term of the form log(1 − z). For <b ≥ 1 we derive a convergent expansion of z−a(1 − z) bBz(a, b) in terms of the function (1 − z) b and of rational functions of z that is uniformly valid for z in any compact set 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 approximations. | en |
| dc.description.sponsorship | This research was supported by Ministerio de Economía, Industria y Competitividad, Gobierno de España, project MTM2017-83490-P, Gobierno de Aragón and European Social Fund (group E24-17R). | en |
| dc.format.extent | 13 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1553/etna_vol48s450 | |
| dc.identifier.issn | 1068-9613 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/31782 | |
| dc.language.iso | eng | en |
| dc.publisher | Kent State University | en |
| dc.publisher | Johann Radon Institute (RICAM) | en |
| dc.relation.ispartof | Electronic Transactions on Numerical Analysis, Volume 48, pp. 450–461, 2018. | 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/ | |
| dc.relation.publisherversion | http://doi.org/10.1553/etna_vol48s450 | |
| dc.rights | © 2018 Kent State University | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Incomplete beta function | en |
| dc.subject | Convergent expansions | en |
| dc.subject | Uniform expansions | en |
| dc.title | Uniform representation of the incomplete beta function 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 | |
| relation.isAuthorOfPublication | 8b28fd50-66f4-431e-a219-43d8c02bb077 | |
| relation.isAuthorOfPublication | e6cd33c5-6d5e-455c-b8da-32a9702e16c8 | |
| relation.isAuthorOfPublication | 93f891c7-529d-4972-8759-9d943c60949c | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b28fd50-66f4-431e-a219-43d8c02bb077 |