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

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.

9 pages

References in corpus (6)

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• Two new proofs of the complete monotonicity of a function involving the psi function
• Some logarithmically completely monotonic functions related to the gamma function
• An extension of an inequality for ratios of gamma functions
• An Inequality for Ratios of Gamma Functions