On the order of convexity for the shifted hypergeometric functions

Li-Mei Wang

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arXiv · 2007.15337

On the order of convexity for the shifted hypergeometric functions

Li-Mei Wang

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Abstract

In the present paper, we study the order of convexity of $z\Gauss(a,b;c;z)$ with real parameters $a, b$ and $c$ where $\Gauss(a,b;c;z)$ is the Gaussian hypergeometric function. First we obtain some conditions for $z\Gauss(a,b;c;z)$ with no any finite orders of convexity by considering its asymptotic behavior around $z=1$. Then the order of convexity of $z\Gauss(a,b;c;z)$ is demonstrated for some ranges of real parameters $a,b$ and $c$. In the last section, we give some examples as the applications of the main results.

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Li-Mei Wang. 2020-07-30. On the order of convexity for the shifted hypergeometric functions. https://arxiv.org/abs/2007.15337

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