## Paul Levrie ; John Campbell - Series acceleration formulas obtained from experimentally discovered hypergeometric recursions

dmtcs:9557 - Discrete Mathematics & Theoretical Computer Science, January 2, 2023, vol. 24, no 2 - https://doi.org/10.46298/dmtcs.9557
Series acceleration formulas obtained from experimentally discovered hypergeometric recursions

Authors: Paul Levrie ; John Campbell

In 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function identities used to obtain series accelerations for values of Dirichlet's $\beta$ function, via the Markov--Wilf--Zeilberger method. Inspired by these past results, together with related results introduced by Chu et al., we introduce a variety of hypergeometric recurrences. We prove these recurrences using the WZ method, and we apply these recurrences to obtain series acceleration identities. We introduce a family of summations generalizing a Ramanujan-type series for $\frac{1}{\pi^2}$ due to Guillera, and a family of summations generalizing an accelerated series for Catalan's constant due to Lupa\c{s}, and many related results.

Volume: vol. 24, no 2
Section: Analysis of Algorithms
Published on: January 2, 2023
Accepted on: December 4, 2022
Submitted on: May 14, 2022
Keywords: [MATH]Mathematics [math]