CERTAIN SUFFICIENCY CONDITIONS ON GAUSSIAN HYPERGEOMETRIC FUNCTIONS

Abstract

ABSTRACT. The author aims at finding certain conditions on a, b and c such that the normalized Gaussian hypergeometric function zF (a, b; c; z) given by ∞ ∑ (a, n)(b, n) F (a, b; c; z) = (c, n)(1, n) zn, |z | < 1, n=0 is in certain subclasses of analytic functions. A particular operator acting on F (a, b; c; z) is also discussed.