Large parameter cases of the Gauss hypergeometric function

Authors:
Nico M. Temme
Affiliations:
CWI, P.O. Box 94079, 1090 GB Amsterdam, Netherlands
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

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Abstract

We consider the asymptotic behavior of the Gauss hypergeometric function when several of the parameters a, b, c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2 functions of unit argument, to explain which difficulties arise in these cases, when standard integrals or differential equations are not available.