%0 Journal Article %T Complete monotonicity of a function involving a ratio of gamma functions and applications %A Feng Qi %A Bai-Ni Guo %J Mathematics %D 2009 %I arXiv %X In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and monotonicity for the ratio of gamma functions}, Taiwanese J. Math. \textbf{7} (2003), no.~2, 239\nobreakdash--247.] and others. As applications, several inequalities involving the volume of the unit ball in $\mathbb{R}^n$ are derived, which refine, generalize and extend some known inequalities. %U http://arxiv.org/abs/0904.1101v3