Simultaneous generation for zeta values by the Markov-WZ method

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 Ap'ery-like formulae for odd zeta values. As a consequence, we get a new identity producing Ap'ery-like series for all $zeta(2n+4m+3), n, mge 0,$ convergent at the geometric rate with ratio $2^{-10}.$