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

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 $\mathbb{U}$ .

Keywords:

Starlike functions, Convex functions, Uniformly Starlike functions, Uniformly Convex functions, Hadamard product Pascal distribution series,

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