A completely monotonic function involving the tri- and tetra-gamma functions

作者：Guo, Bai-Ni^*; Zhao, Jiao-Lian; Qi, Feng

来源：Mathematica Slovaca, 2013, 63(3): 469-478.

DOI：10.2478/s12175-013-0109-2

• completely monotonic function
• tri-gamma function
• tetra-gamma function
• polygamma function
• inequality

The di-gamma function psi(x) is defined on (0,a) by and psi ((i))(x) for i a a"center dot denote the polygamma functions, where I"(x) is the classical Euler's gamma function. In this paper we prove that a function involving the difference between [psi'(x)](2) + psi aEuro(3)(x) and a proper fraction of x is completely monotonic on (0,a).

• 出版日期2013-6
• 单位河南理工大学; 渭南师范学院