A MONOTONICITY PROPERTY INVOLVING THE GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND

被引：71
|
作者：
Yang, Zhen-Hang [1 ]
Chu, Yu-Ming [1 ]
机构：
[1] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2017年 / 20卷 / 03期
关键词：
Gaussian hypergeometric function; generalized elliptic integral; gamma function; psi function; monotonicity;
D O I：
10.7153/mia-20-46
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that the function r -> Y(r) = Ka(r) sin(pi a)r'(2)log(e(R(a)/2)/r') - 1/r'(2) is strictly increasing from (0,1) onto (p/[R(a) sin(pi a)]-1, a(1-a)) for all a is an element of (0,1/2], where r' = root 1- r(2), K-a(r) is the generalized elliptic integral of the first kind, R(a) = -2 gamma -psi(a)-psi(1-a),. is the classical psi function and gamma = 0.57721566 . . . is the Euler-Mascheroni constant.
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页码：729 / 735
页数：7
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