### Series acceleration formulae for beta values

*Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood*

#### Abstract

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).Full Text: PDF PostScript