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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:
 33C05 Classical hypergeometric functions, ${}_2F_1$ 33C45 Orthogonal polynomials and functions of hypergeometric type 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 30C15 Zeros of polynomials, etc. (one complex variable) 41A10 Approximation by polynomials
##### Keywords:
asymptotic expansion; Gauss hypergeometric function
Full Text:
##### References:
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