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.

翻译：Wilf-Zeilberger对是Wilf和Zeilberger在组合恒等式的计算机生成证明算法理论中的核心基础。Wilf-Zeilberger形式是其高维推广形式，可用于证明和发现收敛加速公式。本文对所有可能的有理Wilf-Zeilberger形式给出了结构性描述，该描述可视为经典Ore-Sato定理的加法类比。基于此类比，我们展示了所谓多元超算术项的结构分解，这类项将多元超几何项拓展到了加法场景中。