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)

Source : oai:HAL:hal-00990465v1

Volume: Vol. 12 no. 2

Published on: January 1, 2010

Submitted on: March 26, 2015

Keywords: Dirichlet's beta function,Catalan's constant,Apery-like series,generating function,convergence acceleration,Markov-Wilf-Zeilberger method,Markov-WZ pair,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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