# Extende beta, hypergeometric and confluent hypergeometric functions

## TL;DR

This paper introduces a new extended beta function and explores its properties, leading to the development of extended hypergeometric and confluent hypergeometric functions, with hybrid representations connecting to known special functions.

## Contribution

The paper presents a novel extension of the beta function and its associated hypergeometric functions, including hybrid representations linking to established special functions.

## Key findings

- New extended beta function defined and analyzed.
- Extended hypergeometric functions derived from the new beta function.
- Hybrid representations include known special functions and polynomials.

## Abstract

We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid representations of this extended beta function are derived which include some well known special functions and polynomials.