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arXiv · 2009.13728

Mapping properties of the zero-balanced hypergeometric functions

Li-Mei Wang
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Abstract

In the present paper, the order of convexity of z\Gauss(a,b;c;z) is first given under some conditions on the positive real parameters a, b and c. Then we show that the image domains of the unit disc \D under some shifted zero-balanced hypergeometric functions z\Gauss(a,b;a+b;z) are convex and bounded by two horizontal lines which solves the problem raised by Ponnusamy and Vuorinen in \cite{PonVuor:2001

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Li-Mei Wang. 2020-09-29. Mapping properties of the zero-balanced hypergeometric functions. https://arxiv.org/abs/2009.13728

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