Some Properties of Hypergeometric Functions for Sakaguchi Type Functions

摘要

The Purpose of the present paper is to introduce a subclass S (λ,α,t) and S_T(λ,α,t) of Sakaguchi type functions of order α. Following the works of Merkes, Scott, Ruschewe- yh and Singh ,a sufficient condition for(Gaussian) hypergeometric functions z F (a, b; c; 1) and Silverman , a necessary and sufficient condition for z F (a, b; c; z) in S*(α) is obtained. We determine necessary and sufficient condition for z F (a, b; c; z) to be in S (λ,α,t) and S_T(λ,α,t) under additional restrictions. Furthermore, an integral opera- tor G (a, b; c; z) related to the hypergeometric function is also considered and sufficient condition for S (λ,α,t) and S_T(λ,α,t) are discussed.