Logarithmically completely monotontic functions related the $q-$gamma and the $q-$digamma functions with applications

TL;DR

This paper introduces new classes of logarithmically completely monotonic functions based on $q$-gamma and $q$-digamma functions, deriving inequalities and generalizing existing theorems in the field.

Contribution

It presents novel classes of such functions and extends previous inequalities and theorems related to $q$-gamma and $q$-digamma functions.

Findings

New classes of logarithmically completely monotonic functions are established.

Inequalities for $q$-gamma and $q$-digamma functions are derived.

Generalizations of existing theorems by Alzer, Berg, Chen, and Qi are provided.

Abstract

In this paper we present several new classes of logarithmically completely monotonic functions. Our functions have in common that they are defined in terms of the $q-$gamma and $q-$digamma functions. As an applications of this results, some inequalities for the $q-$gamma and the $q-$digamma functions are established. Some of the given results generalized theorems due to Alzer and Berg and C.-P. Chen and F. Qi.