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Simultaneous generation for zeta values by the Markov-WZ method

Abstract : By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's Apéry-like formulae for odd zeta values. As a consequence, we get a new identity producing Apéry-like series for all ζ(2n+4m+3),n,m ≥ 0, convergent at the geometric rate with ratio 2−10.
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Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood. Simultaneous generation for zeta values by the Markov-WZ method. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, 10 (3), pp.115--123. ⟨hal-00972329⟩

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