A two-parameter deformation of the gamma function, associated functions, and some related inequalities

TL;DR

This paper introduces a new two-parameter deformation of the Gamma function, exploring its properties and deriving inequalities for related functions, thereby extending the understanding of Gamma-type functions.

Contribution

It presents a novel two-parameter deformation of the Gamma function and analyzes its properties and inequalities, expanding the theoretical framework of special functions.

Findings

Defined a new two-parameter Gamma deformation

Derived inequalities for the associated beta and polygamma functions

Extended existing Gamma function properties to the new deformation

Abstract

In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some inequalities for the corresponding beta function and polygamma functions.