Abstract
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)
Highlights
In this paper we continue our study on finding generalized identities [8, 9] that produce fast convergent series for some classical constants
Markov [14] to derive the irrationality of ζ(3) [17]. This series converges at a geometric rate with ratio 1/4
First results related to generating function identities for even zeta values belong to Leshchiner [12] who proved that for |a| < 1
Summary
To cite this version: Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (2), pp.223236. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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