## Mapping properties of analytic function defined by hypergeometric function. II.(English)Zbl 0964.30007

Let $$F(a,b;c;z)$$ denote the Gauss hypergeometric function, let $$\xi(z)=z F(a,b;c;z)$$ and let $$\mu\geq 0$$. In the present paper, mapping properties like starlikeness of the analytic function $$h(z):=(1-\mu) \xi(z)+\mu z \xi'(z)$$ are investigated.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 33C05 Classical hypergeometric functions, $${}_2F_1$$

### Keywords:

starlike functions; convex functions; gamma function