Geometric Properties of the Shifted Hypergeometric Functions |
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| Authors: | Toshiyuki Sugawa Li-Mei Wang |
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| Institution: | 1.Graduate School of Information Sciences,Tohoku University,Aoba-ku, Sendai,Japan;2.School of Statistics,University of International Business and Economics,Beijing,China |
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| Abstract: | We will provide sufficient conditions for the shifted hypergeometric function \(z_2F_1(a,b;c;z)\) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order \(\alpha ,\) \(\lambda \)-spirallikeness of order \(\alpha \) and strong starlikeness of order \(\alpha .\) In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk. |
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