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

摘要

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) = ∑~∞_(n=0)((a)n(b)n)/(?n(1)n)z~n, ∣z∣ < 1, rnis in a certain class of analytic functions. Various results for the particular values of these parameters are deduced.