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

Silverman, H.

J. Math. Anal. Appl. 172, No. 2, 574-581 (1993).

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)].

Reviewer: K.J.Wirths (Braunschweig)

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