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arXiv · 2602.08721

Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds

Kam Cheong Au
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Abstract

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 $\zeta(5,3)$, 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.

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Kam Cheong Au. 2026-02-09. Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds. https://arxiv.org/abs/2602.08721

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