A logarithmically completely monotonic function involving the ratio of gamma functions
Feng Qi, Wen-Hui Li
TL;DR
This paper reviews functions involving gamma ratios, discusses their logarithmic complete monotonicity, and establishes conditions for a new gamma ratio-based function related to coding gain to possess this property.
Contribution
It provides a comprehensive survey and introduces necessary and sufficient conditions for a new gamma ratio function to be logarithmically completely monotonic.
Findings
Identifies conditions for gamma ratio functions to be logarithmically completely monotonic
Provides a survey of existing functions involving gamma functions
Introduces a new gamma ratio function related to coding gain
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.
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