[Submitted on 7 Mar 2024 (v1), last revised 29 Jul 2026 (this version, v4)]

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Abstract:We develop the notion of Wilf-Zeilberger seeds as a powerful framework for generating WZ-pairs and for lifting classical hypergeometric identities to the $q$-setting. As an application, we systematically obtain a large family of $q$-analogues of Ramanujan-type $1/\pi^k$ formulas, extending a body of literature previously limited to sporadic examples. While the majority of these $q$-analogues are modular, we also uncover several curious instances of mock modularity.

Submission history

From: Kam Cheong Au [view email]
[v1] Thu, 7 Mar 2024 14:54:30 UTC (28 KB)
[v2] Mon, 9 Feb 2026 14:37:26 UTC (30 KB)
[v3] Tue, 10 Feb 2026 22:43:18 UTC (30 KB)
[v4] Wed, 29 Jul 2026 07:55:05 UTC (31 KB)

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