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 valuesArticle

Authors: Khodabakhsh Hessami Pilehrood 1; Tatiana Hessami Pilehrood 2

  • 1 Department of Pure Mathematics [Shahrekord]
  • 2 Interactions Plantes Pathogènes


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://doi.org/10.46298/dmtcs.504
Source: HAL:hal-00990465v1
Volume: Vol. 12 no. 2
Published on: January 1, 2010
Imported on: March 26, 2015
Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Dirichlet's beta function, Catalan's constant, Apery-like series, generating function, convergence acceleration, Markov-Wilf-Zeilberger method, Markov-WZ pair

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