Logarithmically Complete Monotonicity of Certain Ratios Involving the $k$-Gamma Function

TL;DR

This paper investigates the logarithmic complete monotonicity of ratios involving the $k$-gamma function, leading to new inequalities and properties relevant to special functions.

Contribution

It establishes the logarithmically complete monotonicity of specific $k$-gamma function ratios, a novel property in this context.

Findings

Proved logarithmic complete monotonicity of certain $k$-gamma ratios

Derived inequalities involving $k$-gamma and $k$-trigamma functions

Enhanced understanding of the monotonicity properties of special functions

Abstract

In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.