Extensions of beta and related functions

TL;DR

This paper introduces a novel extension of the beta function using Bessel-Struve kernel functions and explores its implications for related distributions and hypergeometric functions, providing new properties and potential applications.

Contribution

It presents a new extended beta function based on Bessel-Struve kernels and extends related distributions and hypergeometric functions, offering systematic properties.

Findings

Defined a new extended beta function via Bessel-Struve kernels

Extended beta distribution and hypergeometric functions using the new beta function

Provided properties and potential applications of these extended functions

Abstract

In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the Gauss hypergeometric function and the confluent hypergeometric function in terms of our extended beta function. In addition, some useful properties of these extended functions are also indicated in a systematic way.