Close-to-Convexity properties of Clausen's Hypergeometric Function $_3F_2(a,b,c;d,e;z)$

Abstract

In this paper, we obtain various conditions on the parameters $a,\, b,\, c\,, d$ and $e$ for which the hypergeometric functions $z\,_3F_2(a,b,c;d,e;z)$ to be in the class of all close-to-convex function with respect to some well known convex functions.