How to generate all possible rational Wilf-Zeilberger pairs?

TL;DR

This paper provides a comprehensive structural characterization of all rational Wilf-Zeilberger pairs and their continuous and mixed variants, advancing the understanding of their algebraic and combinatorial properties.

Contribution

It introduces a complete structural description of all rational Wilf-Zeilberger pairs and their analogues, filling a gap in the theoretical framework.

Findings

Characterization of all rational Wilf-Zeilberger pairs

Extension to continuous and mixed analogues

Structural insights into algebraic properties

Abstract

A Wilf--Zeilberger pair $(F, G)$ in the discrete case satisfies the equation $ F(n+1, k) - F(n, k) = G(n, k+1) - G(n, k)$. We present a structural description of all possible rational Wilf--Zeilberger pairs and their continuous and mixed analogues.