eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2010-01-01
Vol. 12 no. 2
10.46298/dmtcs.504
504
journal article
Series acceleration formulas for beta values
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)
https://dmtcs.episciences.org/504/pdf
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]