Complete monotonicity of a function involving a ratio of gamma functions and applications

Details Complete monotonicity of a function involving a ratio of gamma functions and applications Complete monotonicity of a function involving a ratio of gamma functions and applications

2009-04-07

arxiv.org/abs/0904.1101v3

Banach Journal of Mathematical Analysis 6, no. 1, 35-44 (2012)

Mathematics

Classical Analysis and ODEs

9 pages

Scientific paper

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.

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