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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:
30C45Special classes of univalent and multivalent functions
33C20Generalized hypergeometric series, p F q
33C05Classical hypergeometric functions, 2 F 1