How to generate all possible rational Wilf-Zeilberger forms?
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908398028587008 |
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| author | Chen, Shaoshi Koutschan, Christoph Wang, Yisen |
| author_facet | Chen, Shaoshi Koutschan, Christoph Wang, Yisen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to generate all possible rational Wilf-Zeilberger forms? Chen, Shaoshi Koutschan, Christoph Wang, Yisen Symbolic Computation 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. |
| title | How to generate all possible rational Wilf-Zeilberger forms? |
| topic | Symbolic Computation |
| url | https://arxiv.org/abs/2405.02430 |