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Large parameter cases of the Gauss hypergeometric function. (English) Zbl 1019.33003
The author considers the asymptotic behavior of the Gauss hypergeometric function with several of the parameters $a,b,c$ are large. The author indicates which cases are already available and which cases need more attention. There are also a few examples of $_2F_3$ functions of unit argument, to explain which difficulties arise in these cases when standard integrals or differential equations are not available.

MSC:
33C05Classical hypergeometric functions, ${}_2F_1$
33C45Orthogonal polynomials and functions of hypergeometric type
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
30C15Zeros of polynomials, etc. (one complex variable)
41A10Approximation by polynomials
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