Discrete Mathematics & Theoretical Computer Science, Vol 12, No 2 (2010)

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Series acceleration formulae for beta values

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood


We prove generating function identities producing fast convergent series for the sequences β(2n+1), β(2n+2) and β(2n+3), where β 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 ζ(3).

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