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arXiv · 2502.15249

Three-parameter generalizations of formulas due to Guillera

John M. Campbell
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Abstract

Guillera has introduced remarkable series expansions for $\frac{1}{\pi^2}$ of convergence rates $-\frac{1}{1024}$ and $-\frac{1}{4}$ via the Wilf-Zeilberger method. Through an acceleration method based on Zeilberger's algorithm and related to Chu and Zhang's series accelerations based on Dougall's ${}_{5}H_{5}$-series, we introduce and prove three-parameter generalizations of Guillera's formulas. We apply our method to construct rational, hypergeometric series for $\frac{1}{\pi^2}$ that are of the same convergence rates as Guillera's series and that have not previously been known.

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John M. Campbell. 2025-02-21. Three-parameter generalizations of formulas due to Guillera. https://arxiv.org/abs/2502.15249

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