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  Volume 5, Issue 4, Article 83
 
Certain Sufficiency Conditions on Gaussian Hypergeometric Functions
    Authors: Anbhu Swaminathan,  
    Keywords: Gaussian hypergeometric functions, Convex functions, Starlike functions  
    Date Received: 20/02/04  
    Date Accepted: 19/06/04  
    Subject Codes:

30C45, 33C45, 33A30

  
    Editors: Herb Silverman,  
 
    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 begin{equation*} F(a,b;c;z)=sum_{n=0}^{infty} frac{(a,n)(b,n)}{(c,n)(1,n)}z^n, quad vert zvert1, end{equation*} is in certain subclasses of analytic functions. A particular operator acting on $F(a,b;c;z)$ is also discussed.

         
       
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