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Zbl 0667.33002
Wagner, Eberhard
Asymptotische Entwicklungen der hypergeometrischen Funktion $F(a,b,c,z)$ für $\vert c\vert \to \infty$ und konstante Werte a,b und z. (Asymptotic expansions of the hypergeometric function $F(a,b,c,z)$ for $\vert c\vert \to \infty$ and constant values a,b and z.). (German)
[J] Demonstr. Math. 21, No.2, 441-458 (1988). ISSN 0420-1213

The paper gives asymptotic expansions of the Gauss hypergeometric function $F(a,b,c,z)$ for large complex values of c, with constant arbitrary values of the other parameters, and $\vert \arg (1-z)\vert \le \pi$. In this way a substantial improvement is given of earlier results of, for instance, Watson and Perron.
[N.M.Temme]

MSC 2000:: *33C05 Classical hypergeometric functions
41A60 Asymptotic problems in approximation
30E15 Asymptotic representations in the complex domain

Keywords: Gauss hypergeometric function

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