The Gauss hypergeometric function F (a, b; c; z) for large c

Authors:
Chelo Ferreira;José L. López;Ester Pérez Sinusía
Affiliations:
Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain;Departamento de Matemática e Informática, Universidad Pública de Navarra, Pamphma, Spain;Departamento de Matemática e Informática, Universidad Pública de Navarra, Pamphma, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We consider the Gauss hypergeometric function F(a,b+1; c+2; z) for a,b,c ∈ C c ≠ -2, -3-4,... and |arg(1 - z)|F(a,b + 1; c + 2; z) in terms of rational functions of a, b, c and z valid for |b||z| c - bz| and |c - b||z| c - bz|. This expansion has the additional property of being asymptotic for large c with fixed a uniformly in b and z (with bounded b/c). Moreover, the asymptotic character of the expansion holds for a larger set of b, c and z specified below.