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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.15249 |
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Table of Contents:
- Guillera has introduced remarkable series expansions for $\frac{1}{π^2}$ 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 $\frac{1}{π^2}$ that are of the same convergence rates as Guillera's series and that have not previously been known.