论文标题
在移动的超几何函数的凸度顺序
On the order of convexity for the shifted hypergeometric functions
论文作者
论文摘要
在本文中，我们研究了$ z \ gauss（a，b; c; c; z）$的凸度顺序，其中带有实际参数$ a，b $和$ c $其中$ \ gauss（a，b; c; c; z）$是高斯的超角函数。首先，我们通过考虑其渐近行为左右$ z = 1 $，获得了$ z \ gauss（a，b; c; z）$的一些条件，没有任何有限的凸订单。然后，对于一些实际参数$ a，b $和$ c $的范围，证明了$ z \ gauss（a，b; c; z）$的凸的顺序。在最后一部分中，我们给出一些示例作为主要结果的应用。
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.
