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 $\mathbb{U}$ . 

Keywords

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

References

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