Application of Pascal Distribution Series to Ronning Type Starlike and Convex Functions

Abstract

In this article we investigate the connections between the Pascal distribution series and the class of analytic functions $ f $ normalized by $ f ( 0 ) = f ' ( 0 ) - 1 = 0 $ in the open unit disk $ \mathbb { U } = \left \{ z \in \mathbb { C } : | z | < 1 \right \} $ and its coefficients are probabilities of the Pascal distribution.More precisely ,we determine such connection with parabolic starlike and uniformly convex functions in the open unit disk $\mathbb{U}$ .