A short proof of duality relations for hypergeometric functions

TL;DR

This paper presents a simple algebraic method based on the non-local derangement identity to derive duality relations for hypergeometric functions, offering an alternative to existing approaches.

Contribution

It introduces a straightforward algebraic technique to establish duality relations for hypergeometric functions, expanding the toolkit beyond previous methods.

Findings

Derived duality relations using a new algebraic approach

Simplified proof technique compared to prior methods

Applicable to a broad family of hypergeometric identities

Abstract

Identities involving finite sums of products of hypergeometric functions and their duals have been studied since 1930s. Recently Beukers and Jouhet have used an algebraic approach to derive a very general family of duality relations. In this paper we provide an alternative way of obtaining such results. Our method is very simple and it is based on the non-local derangement identity.