Ferreira González, CheloLópez García, José LuisPérez Sinusía, Ester2018-12-142018-12-1420181068-961310.1553/etna_vol48s450https://academica-e.unavarra.es/handle/2454/31782We 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.13 p.application/pdfeng© 2018 Kent State UniversityIncomplete beta functionConvergent expansionsUniform expansionsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess