The BiGamma Function and some of its Related Inequalities

TL;DR

This paper introduces the BiGamma function, explores its properties and relationships with the Beta function, and establishes inequalities for approximation, expanding the mathematical understanding of gamma-related functions.

Contribution

It defines the BiGamma function as a new generalization of Euler's gamma function and investigates its properties and inequalities.

Findings

BiGamma function linked to Beta function

Derived inequalities for approximation

Extended properties of gamma functions

Abstract

In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new function to the standard Beta function have been provided. We have also established inequalities, which allow to approximate this new function.