A logarithmically completely monotonic function involving the ratio of gamma functions

Abstract

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient conditions for a new function involving the ratio of two gamma functions and originating from the coding gain to be logarithmically completely monotonic.

arXiv comment11 pages

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Cited by in corpus (6)

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• From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
• A ratio of many gamma functions and its properties with applications
• Some inequalities for the trigamma function in terms of the digamma function
• Logarithmic complete monotonicity of a matrix-parametrized analogue of the multinomial distribution
• An inequality involving the gamma and digamma functions