Large Parameter Cases of the Gauss Hypergeometric Function

Details Large Parameter Cases of the Gauss Hypergeometric Function Large Parameter Cases of the Gauss Hypergeometric Function

2002-05-07

arxiv.org/abs/math/0205065v1

Mathematics

Classical Analysis and ODEs

21 pages, 4 figures

Scientific paper

We consider the asymptotic behaviour 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 Krawtchouk, Meixner, 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.

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