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arXiv · 2604.15172

Evaluations of some series via the WZ method

Qing-Hu Hou·Zhi-Wei Sun
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Abstract

In this paper, we evaluate some series via the WZ method, and confirm several previous conjectures. For example, we prove the following two identities conjectured by the second author: $$\sum_{k=0}^{\infty} \frac{(28k^2 + 10k + 1) \binom{2k}{k}^5}{(6k + 1)(-64)^k \binom{3k}{k} \binom{6k}{3k}} = \frac{3}π$$ and $$\sum_{k=1}^\infty \frac{d^4}{dk^4}\left(\frac{(21k-8)Γ(k+1)^2}{k^3Γ(2k+1)}\right)=\frac{1959}2ζ(6)-432ζ(3)^2. $$

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Qing-Hu Hou, Zhi-Wei Sun. 2026-04-16. Evaluations of some series via the WZ method. https://arxiv.org/abs/2604.15172

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