LANDEN INEQUALITIES FOR A CLASS OF HYPERGEOMETRIC FUNCTIONS WITH APPLICATIONS
LANDEN INEQUALITIES FOR A CLASS OF HYPERGEOMETRIC FUNCTIONS WITH APPLICATIONS
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一类超几何函数的兰登不等式及其应用
DOI：
10.7153/mia-2018-21-38
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发表时间：
2018-04-01
影响因子：
1
通讯作者：
Chu, Yu-Ming
中科院分区：
文献类型：
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作者：
Wang, Miao-Kun;Chu, Yu-Ming
在本文中，我们研究一类高斯超几何函数 F-2(1)(a, b; (a + b + 1)/2; x)(a, b > 0)，并找到第一象限中 ab 平面的最大区域，其中第一类完全椭圆积分的著名兰登恒等式对 (0,1) 的每个 x 子集有效。此外，引入了具有两个参数mu(a,b)(r)的广义Grotzsch环函数，并推导了Grotzsch环函数mu(r)对于mu(a,b)(r)满足的重复公式的不等式形式的类似物。
In this paper, we study a class of Gaussian hypergeometric function F-2(1)(a, b; (a + b + 1)/2; x)(a, b > 0), and find the maximal regions of ab plane in the first quadrant where the well-known Landen identities for the complete elliptic integrals of the first kind turn on respective inequalities valid for each x subset of (0,1). Besides, the generalized Grotzsch ring function with two parameters mu(a,b)(r) is introduced, and the analogs of duplication formula satisfied by Grotzsch ring function mu(r) for mu(a,b)(r), in the form of inequalities, will be derived.