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Pré-Publication, Document De Travail Année : 2022

Series acceleration formulas obtained from experimentally discovered hypergeometric recursions

Paul Levrie
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Résumé

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.
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Dates et versions

hal-03659300 , version 1 (04-05-2022)
hal-03659300 , version 2 (05-11-2022)
hal-03659300 , version 3 (20-12-2022)

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  • HAL Id : hal-03659300 , version 2

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Paul Levrie, John Campbell. Series acceleration formulas obtained from experimentally discovered hypergeometric recursions. 2022. ⟨hal-03659300v2⟩
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