87789 20200217152413.0 doi 10.1553/etna_vol48s450 sideral 116074 ART-2018-116074 eng (orcid)0000-0002-3698-6719 Ferreira, Chelo Universidad de Zaragoza Uniform representations of the incomplete beta function in terms of elementary functions 2018 Access copy available to the general public Unrestricted We consider the incomplete beta function $B_{z}(a,b)$ in the maximum domain ofanalyticity of its three variables: $a,b,z\\in\\mathbb{C}$, $-a\\notin\\mathbb{N}$,$z\\notin[1,\\infty)$. For $\\Re b\\le 1$ we derive a convergent expansion of$z^{-a}B_{z}(a,b)$ in terms of the function $(1-z)^b$ and of rational functionsof $z$ that is uniformly valid for $z$ in any compact set in$\\mathbb{C}\\setminus[1,\\infty)$. When $-b\\in \\mathbb{N}\\cup\\{0\\}$, the expansionalso contains a logarithmic term of the form $\\log(1-z)$. For $\\Re b\\ge 1$ wederive a convergent expansion of $z^{-a}(1-z)^bB_{z}(a,b)$ in terms of thefunction $(1-z)^b$ and of rational functions of $z$ that is uniformly valid for$z$ in any compact set in the exterior of the circle $\\vert z-1\\vert=r$ forarbitrary $r>0$. The expansions are accompanied by realistic error bounds. Somenumerical experiments show the accuracy of the approximations. info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R info:eu-repo/grantAgreement/ES/IUMA/MTM2017-83490-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.475 2018 MATHEMATICS, APPLIED 76 / 254 = 0.299 2018 Q2 T1 0.953 2018 Analysis 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion López, José L. (orcid)0000-0002-8021-2745 Pérez Sinusía, Ester Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 48 (2018), 450-461 Electron. trans. numer. anal. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 1068-9613 450752 http://zaguan.unizar.es/record/87789/files/texto_completo.pdf Versión publicada 411965 http://zaguan.unizar.es/record/87789/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:87789 articulos driver 2020-02-17-13:02:13 ARTICLE