How to generate all possible rational Wilf-Zeilberger forms?
Symbolic Computation
2025-06-10 v2
Abstract
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their high-dimensional generalizations, which can be used for proving and discovering convergence acceleration formulas. This paper presents a structural description of all possible rational such forms, which can be viewed as an additive analog of the classical Ore-Sato theorem. Based on this analog, we show a structural decomposition of so-called multivariate hyperarithmetic terms, which extend multivariate hypergeometric terms to the additive setting.
Keywords
Cite
@article{arxiv.2405.02430,
title = {How to generate all possible rational Wilf-Zeilberger forms?},
author = {Shaoshi Chen and Christoph Koutschan and Yisen Wang},
journal= {arXiv preprint arXiv:2405.02430},
year = {2025}
}