Simultaneous generation for zeta values by the Markov-WZ method

Pilehrood, Khodabakhsh Hessami; Pilehrood, Tatiana Hessami

doi:10.46298/dmtcs.424

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…which is known as Amdeberhan's formula for ζ (3), see [7] for more details. Then, Pilehrood and Pilehrood (2010) [46] arrived at the following expression Clearly, there are other series representations for ζ (3), and there are ongoing investigations in this direction. It is important to point out that the main result obtained in this work improves the convergence in comparison with the aforementioned results.…”

Section: Introductionmentioning

confidence: 99%

A single parameter Hermite-Padé series representations for Apéry's constant

Soria-Lorente,

Berres

2018

Preprint

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Inspired by the results of Rhin and Viola (2001), the purpose of this work is to elaborate on a series representation for ζ (3) which only depends on one single integer parameter. This is accomplished by deducing a Hermite-Padé approximation problem using ideas of Sorokin (1998). As a consequence we get a new recurrence relation for the approximation of ζ(3) as well as a corresponding new continued fraction expansion for ζ(3), which do no reproduce Apéry's phenomenon, i.e., though the approaches are different, they lead to the same sequence of diophantine approximations to ζ (3). Finally, the convergence rates of several series representations of ζ(3) are compared.

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Section: Introductionmentioning

confidence: 99%

A single parameter Hermite-Padé series representations for Apéry's constant

Soria-Lorente,

Berres

2018

Preprint

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Bivariate Identities for Values of the Hurwitz Zeta Function and Supercongruences

Pilehrood¹,

Pilehrood²

2012

Electron. J. Combin.

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In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting formulas related to values of the Hurwitz zeta function. We also get an extension of the bivariate identity of Cohen to values of the Hurwitz zeta function. The main tool we use here is a construction of new Markov-WZ pairs. As application of our results, we prove several conjectures on supercongruences proposed by J. Guillera, W. Zudilin, and Z. W. Sun.

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Series acceleration formulas for beta values

Pilehrood¹,

Pilehrood

2010

Discrete Mathematics &Amp; Theoretical Computer Science

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International audience 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)

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Simultaneous generation for zeta values by the Markov-WZ method

Cited by 4 publications

References 11 publications

A single parameter Hermite-Padé series representations for Apéry's constant

A single parameter Hermite-Padé series representations for Apéry's constant

Bivariate Identities for Values of the Hurwitz Zeta Function and Supercongruences

Series acceleration formulas for beta values

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