Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds
Number Theory
2026-02-10 v1 Combinatorics
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 , 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.
Cite
@article{arxiv.2602.08721,
title = {Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds},
author = {Kam Cheong Au},
journal= {arXiv preprint arXiv:2602.08721},
year = {2026}
}