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arXiv · 2212.09965

Series acceleration formulas obtained from experimentally discovered hypergeometric recursions

Paul Levrie·John Campbell
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Abstract

In 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function identities used to obtain series accelerations for values of Dirichlet's $β$ 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 $\frac{1}{π^2}$ due to Guillera, and a family of summations generalizing an accelerated series for Catalan's constant due to Lupaş, and many related results.

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Paul Levrie, John Campbell. 2022-12-20. Series acceleration formulas obtained from experimentally discovered hypergeometric recursions. https://arxiv.org/abs/2212.09965

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