Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917260379029504 |
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| author | Au, Kam Cheong |
| author_facet | Au, Kam Cheong |
| contents | By extracting coefficients from Wilf-Zeilberger pairs with respect to auxiliary parameters, we discover many nontrivial hypergeometric series involving harmonic numbers. In particular, we obtain a rapidly convergent series for the depth-two multiple zeta value $ζ(5,3)$, which appears to be the first result of its kind in the literature. We also experiment with the Hilbert-Poincare series attached with a WZ-seed and conjecture that it admits a remarkably simple form, suggesting the presence of an underlying graded algebra structure behind WZ-seeds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08721 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds Au, Kam Cheong Number Theory Combinatorics 11B65, 11M32, 33C20 (Primay) 33F10 (Secondary) By extracting coefficients from Wilf-Zeilberger pairs with respect to auxiliary parameters, we discover many nontrivial hypergeometric series involving harmonic numbers. In particular, we obtain a rapidly convergent series for the depth-two multiple zeta value $ζ(5,3)$, which appears to be the first result of its kind in the literature. We also experiment with the Hilbert-Poincare series attached with a WZ-seed and conjecture that it admits a remarkably simple form, suggesting the presence of an underlying graded algebra structure behind WZ-seeds. |
| title | Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds |
| topic | Number Theory Combinatorics 11B65, 11M32, 33C20 (Primay) 33F10 (Secondary) |
| url | https://arxiv.org/abs/2602.08721 |