Some integrals of hypergeometric functions

TL;DR

This paper investigates a specific definite integral involving two hypergeometric functions with complex arguments and reveals that the integral's value is independent of the functions' parameters.

Contribution

It demonstrates a surprising parameter independence in a class of integrals involving hypergeometric functions, which was previously unknown.

Findings

The integral's value is independent of hypergeometric parameters.

The integral involves classical hypergeometric functions with complicated arguments.

The result simplifies the understanding of such integrals.

Abstract

We consider a certain definite integral involving the product of two classical hypergeometric functions having complicated arguments. We show in this paper the surprising fact that this integral does not depend on the parameters of the hypergeometric functions.