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,ba,b and cc such that the normalized Gaussian hypergeometric function zF(a,b;c;z)zF(a,b;c;z) given by F(a,b;c;z)=∑n=0∞(a)n(b)n(c)n(1)nzn,|z|<1, is in a certain class of analytic functions. Various results for the particular values of these parameters are deduced.