A MONOTONICITY PROPERTY INVOLVING THE GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND
A MONOTONICITY PROPERTY INVOLVING THE GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND
复制标题
涉及第一类广义椭圆积分的单调性
DOI：
10.7153/mia-20-46
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发表时间：
2017-07-01
影响因子：
1
通讯作者：
Chu, Yu-Ming
中科院分区：
文献类型：
--
作者：
Yang, Zhen-Hang;Chu, Yu-Ming
本文证明了函数-> Y(r) = Ka(r) sin(a)r'(2)log(e(r(a)/2)/r') -1 /r'(2)从（0,1）严格递增到(p/[r(a) sin（a)]-1, a(1-a)）对于所有a是(0,1/2]的一个元素，其中r' =根1- r(2), K-a(r)是第一类广义椭圆积分，r(a) = -2 γ -psi(a)-psi(1-a)，是经典的psi函数和γ = 0.57721566…是欧拉-马斯切罗尼常数。
In this paper, we prove that the functionr -> 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.