000087789 001__ 87789
000087789 005__ 20200217152413.0
000087789 0247_ $$2doi$$a10.1553/etna_vol48s450
000087789 0248_ $$2sideral$$a116074
000087789 037__ $$aART-2018-116074
000087789 041__ $$aeng
000087789 100__ $$0(orcid)0000-0002-3698-6719$$aFerreira, Chelo$$uUniversidad de Zaragoza
000087789 245__ $$aUniform representations of the incomplete beta function in terms of elementary functions
000087789 260__ $$c2018
000087789 5060_ $$aAccess copy available to the general public$$fUnrestricted
000087789 5203_ $$aWe 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.
000087789 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/ES/IUMA/MTM2017-83490-P
000087789 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000087789 590__ $$a1.475$$b2018
000087789 591__ $$aMATHEMATICS, APPLIED$$b76 / 254 = 0.299$$c2018$$dQ2$$eT1
000087789 592__ $$a0.953$$b2018
000087789 593__ $$aAnalysis$$c2018$$dQ2
000087789 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000087789 700__ $$aLópez, José L.
000087789 700__ $$0(orcid)0000-0002-8021-2745$$aPérez Sinusía, Ester$$uUniversidad de Zaragoza
000087789 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000087789 773__ $$g48 (2018), 450-461$$pElectron. trans. numer. anal.$$tELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS$$x1068-9613
000087789 8564_ $$s450752$$uhttps://zaguan.unizar.es/record/87789/files/texto_completo.pdf$$yVersión publicada
000087789 8564_ $$s411965$$uhttps://zaguan.unizar.es/record/87789/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000087789 909CO $$ooai:zaguan.unizar.es:87789$$particulos$$pdriver
000087789 951__ $$a2020-02-17-13:02:13
000087789 980__ $$aARTICLE