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,b;c;z) given by F(a,b;c;z)[email protected]?n=0~(a)"n(b)"n(c)"n(1)"nz^n,|z|<1, is in a certain class of analytic functions. Various results for the particular values of these parameters are deduced.