Three-parameter generalizations of formulas due to Guillera
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910838026141696 |
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| author | Campbell, John M. |
| author_facet | Campbell, John M. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-parameter generalizations of formulas due to Guillera Campbell, John M. Classical Analysis and ODEs 33F10 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. |
| title | Three-parameter generalizations of formulas due to Guillera |
| topic | Classical Analysis and ODEs 33F10 |
| url | https://arxiv.org/abs/2502.15249 |