Simultaneous generation for zeta values by the Markov-WZ method

Khodabakhsh Hessami Pilehrood (1) , Tatiana Hessami Pilehrood (1)

1 Department of Pure Mathematics [Shahrekord]

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.

Domaines: Mathématique discrète [cs.DM]

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood. Simultaneous generation for zeta values by the Markov-WZ method. Discrete Mathematics and Theoretical Computer Science, 2008, Vol. 10 no. 3 (3), pp.115--123. ⟨10.46298/dmtcs.424⟩. ⟨hal-00972329⟩