Monotonicity properties of a function involving the psi function with applications
Monotonicity properties of a function involving the psi function with applications
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涉及 psi 函数及其应用的函数的单调性属性
DOI：
10.1186/s13660-015-0724-2
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发表时间：
2015-06-13
影响因子：
1.6
通讯作者：
Chu, Yu-Ming
中科院分区：
文献类型：
--
作者：
Zhao, Tie-Hong;Yang, Zhen-Hang;Chu, Yu-Ming
在本文中，我们提出了最佳可能的参数a是(1/5，无穷)的元素，使得函数psi‘(x+1)-L-x(x，a)和psi’‘(x+1)-L-xx(x，a)关于x是严格增减的，其中L(x，A)=1/90a(2)+2log(x(2)+x+3a+1/3)+45a(2)/90a(2)+2log(x(2)+x+15a-1/45a)，psi(X)是经典的psi函数。作为应用，我们得到了psi函数及其导数的几个新的锐界。
In this paper, we present the best possible parameter a is an element of (1/5, infinity) such that the functions psi' (x + 1) - L-x(x,a) and psi ''(x + 1) - L-xx(x,a) are strictly increasing or decreasing with respect to x is an element of(0,infinity), where L(x,a) = 1/90a(2)+2 log(x(2) + x + 3a+1/3) + 45a(2)/90a(2)+2 log(x(2) + x + 15a-1/45a) and psi(x) is the classical psi function. As applications, we get several new sharp bounds for the psi function and its derivatives.