How to generate all possible rational Wilf-Zeilberger pairs?

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.

17 pages, add the notion of pseudo residues in the differential case, and some related papers in the reference, ACMES special volume in the Fields Institute Communications series, 2018