# A remarkable double integral of the product of two Gaussian hypergeometric functions

## TL;DR

This paper introduces a novel double integral involving two Gaussian hypergeometric functions, computed through two different methods, and equates the results to derive the integral, contributing new analytical techniques.

## Contribution

The paper presents a new approach to evaluate a previously unstudied double integral of Gaussian hypergeometric functions using two distinct methods.

## Key findings

- Derived the double integral using two different methods
- Established equivalence of results to solve the integral
- Contributed a new integral expression to mathematical literature

## Abstract

In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed by two methods. The first method gives a combination of hypergeometric functions and the requested original integral, while with the second method this different integral can be computed directly. Equalization of the results from both methods gives the requested integral.