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arXiv · 0904.1101

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

Feng Qi·Bai-Ni Guo
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Abstract

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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Feng Qi, Bai-Ni Guo. 2011-01-25. Complete monotonicity of a function involving a ratio of gamma functions and applications. https://arxiv.org/abs/0904.1101

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