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Starlike and convexity properties for hypergeometric functions. (English) Zbl 0774.30015

Let \(F(a,b;c;z)\) denote the classical hypergeometric function. The author derives conditions for \(zF(a,b;c;z)\) to belong to various subclasses of the class of holomorphic functions univalent in the unit disk. As a further reference on these problems the reader may compare: S. S. Miller and P. T. Mocanu, Univalence of Gaussian and confluent hypergeometric functions, [Proc. Am. Math. Soc. 110, No. 2, 333-342 (1990; Zbl 0707.30012)].

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C05 Classical hypergeometric functions, \({}_2F_1\)

Citations:

Zbl 0707.30012
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