Geodesic
Series acceleration formulas obtained from experimentally discovered hypergeometric recursions
Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 2.

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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.
DOI : 10.46298/dmtcs.9557
Classification : 05A15, 11Y60, 33C20, 33F10, 40A05, 41A25 
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Levrie, Paul; Campbell, John. Series acceleration formulas obtained from experimentally discovered hypergeometric recursions. Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 2. doi : 10.46298/dmtcs.9557. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9557/

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