Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions

The author aims at finding certain conditions on the parameters a; b and c such that the normalized Gaussian hypergeometric function zF .a; bI cI z/ given by F .a; bI cI z/ D 1X nD0 .a/n.b/n .c/n.1/n zn; jzj < 1; is in a certain class of analytic functions. Various results for the particular values of these parameters are deduced.