Starlike and Convexity Properties for Hypergeometric Functions

Given the hypergeometric function F(a, b; c; z) = ∑∞n = 0 ((a)n (b)n/(c)n(1)n) zn, we place conditions on a, b, c to guarantee that zF(a, b; c; z) will be in various subclasses of starlike and convex functions. Further constraints lead to coefficient characterizations of the families. Operators related to the hypergeometric function are also examined.