2025/02/21 by Campbell, John M.
#33F10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.15249
Guillera has introduced remarkable series expansions for (1)/(π2) of convergence rates -(1)/(1024) and -(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 5H5-series, we introduce and prove three-parameter generalizations of Guillera's formulas. We apply our method to construct rational, hypergeometric series for (1)/(π2) that are of the same convergence rates as Guillera's series and that have not previously been known.