An inequality involving the gamma and digamma functions

TL;DR

This paper establishes a new inequality involving gamma and digamma functions and uses it to analyze the negativity and monotonicity of related functions, contributing to the understanding of special functions.

Contribution

The paper introduces a novel inequality for gamma and digamma functions and applies it to prove properties like negativity and monotonicity of certain functions involving these special functions.

Findings

Proved a new inequality involving gamma and digamma functions.

Demonstrated negativity of a specific function involving these functions.

Established monotonicity properties of related functions.

Abstract

In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.