Further Inequalities Associated with the Classical Gamma Function

TL;DR

This paper establishes new double inequalities related to ratios of the classical Gamma function, extending previous results through monotonicity properties of generalized Gamma functions.

Contribution

It introduces generalized inequalities for the Gamma function ratios using monotonicity, broadening the scope of existing inequalities.

Findings

Derived new double inequalities for Gamma function ratios

Generalized previous inequalities using monotonicity properties

Proposed open problems for future research

Abstract

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions involving the the generalized Gamma functions. At the end, we pose some open problems.