publication . Article . Journal . 2018

Uniform representations of the incomplete beta function in terms of elementary functions

José Luis López García; Chelo Ferreira; Ester Pérez Sinusía;
Open Access
  • Published: 03 Dec 2018 Journal: ETNA - Electronic Transactions on Numerical Analysis, volume 48, pages 450-461 (issn: 1068-9613, eissn: 1068-9613, Copyright policy)
  • Publisher: Osterreichische Akademie der Wissenschaften
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....
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Subjects
free text keywords: Incomplete beta function, Convergent expansions, Uniform expansions, incomplete beta function, convergent expansions, uniform expansions,Mathematik, Mathematical economics, Mathematics, Uniform representation, European Social Fund, Beta function, symbols.namesake, symbols, Elementary function
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