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Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions. (English) Zbl 1189.33008

Summary: The author aims at finding certain conditions on the parameters \(a,b\) and \(c\) such that the normalized Gaussian hypergeometric function \(zF(a,b;c;z)\) given by \[ F(a,b;c;z=\sum_{n=0}^{\infty}\frac{(a)_n(b)_n}{(c)_n(1)_n} z^n, ~|z|<1, \] is in a certain class of analytic functions. Various results forthe particular values of these parameters are deduced.

MSC:

33C05 Classical hypergeometric functions, \({}_2F_1\)
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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References:

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