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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, \({}_2F_1\)
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