J. Aust. Math. Soc.  80 (2006), 81-88
Some completely monotonic functions involving the gamma and polygamma functions

Feng Qi
  Research Institute of Mathematical Inequality Theory
  Henan Polytechnic University
  Jiaozuo City
  Henan Province 454010
  China
  qifeng@hpu.edu.cn
Bai-Ni Guo
  Research Institute of Mathematical Inequality Theory
  Henan Polytechnic University
  Jiaozuo City
  Henan Province 454010
  China
  guobaini@hpu.edu.cn
and
Chao-Ping Chen
  Research Institute of Mathematical Inequality Theory
  Henan Polytechnic University
  Jiaozuo City
  Henan Province 454010
  China
  chenchaoping@hpu.edu.cn


Abstract
The function ${[\Gamma(x+1)]^{1/x}}(1+1/x)^x/x$ is strictly logarithmically completely monotonic in $(0,\infty)$ . The function $\psi''(x+2)+{(1+x^2)}/{x^2(1+x)^2}$ is strictly completely monotonic in $(0,\infty)$ .
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