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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2010

Series acceleration formulas for beta values

Abstract

We prove generating function identities producing fast convergent series for the sequences beta(2n + 1); beta(2n + 2) and beta(2n + 3), where beta is Dirichlet's beta function. In particular, we obtain a new accelerated series for Catalan's constant convergent at a geometric rate with ratio 2(-10); which can be considered as an analog of Amdeberhan-Zeilberger's series for zeta(3)
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Dates and versions

hal-00990465 , version 1 (13-05-2014)

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Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood. Series acceleration formulas for beta values. Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 2 (2), pp.223-236. ⟨10.46298/dmtcs.504⟩. ⟨hal-00990465⟩
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