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arXiv · 2405.02430

How to generate all possible rational Wilf-Zeilberger forms?

Shaoshi Chen·Christoph Koutschan·Yisen Wang
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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.

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Shaoshi Chen, Christoph Koutschan, Yisen Wang. 2024-05-03. How to generate all possible rational Wilf-Zeilberger forms?. https://arxiv.org/abs/2405.02430

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