Large parameter cases of the Gauss hypergeometric function

Abstract

We consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters {it 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 ${}_3${it F}${}_2$ functions of unit argument, to explain which difficulties arise in these cases, when standardintegrals or differential equations are not available