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 $\zeta (2n+4m+3),$ $n,m\ge 0,$ convergent at the geometric rate with ratio $2^{-10}.$

arXiv comment7 pages