Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Campbell, John M.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979236940
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