## Khodabakhsh Hessami Pilehrood ; Tatiana Hessami Pilehrood - Series acceleration formulas for beta values

dmtcs:504 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 2 - https://doi.org/10.46298/dmtcs.504
Series acceleration formulas for beta values

Authors: Khodabakhsh Hessami Pilehrood ; Tatiana Hessami Pilehrood

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)

Volume: Vol. 12 no. 2
Published on: January 1, 2010
Imported 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]