{"docId":504,"paperId":504,"url":"https:\/\/dmtcs.episciences.org\/504","doi":"10.46298\/dmtcs.504","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":89,"name":"Vol. 12 no. 2"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-00990465","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-00990465v1","dateSubmitted":"2015-03-26 16:20:59","dateAccepted":"2015-06-09 14:47:40","datePublished":"2010-01-01 08:00:00","titles":{"en":"Series acceleration formulas for beta values"},"authors":["Pilehrood, Khodabakhsh Hessami","Pilehrood, Tatiana Hessami"],"abstracts":{"en":"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)"},"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]"]}