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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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https://hal.inria.fr/hal-00990465
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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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