More supplements to a class of logarithmically completely monotonic functions associated with the gamma function

Senlin Guo, Feng Qi

Published 2009-04-26Version 1

In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on $(0,\infty)$. As applications of the necessary and sufficient condition, some inequalities for bounding the psi and polygamma functions and the ratio of two gamma functions are derived.