Simultaneous generation for zeta values by the Markov-WZ method

TL;DR

This paper uses the Markov-WZ method to derive new identities for odd zeta values, including generalizations of known formulas, and presents rapidly convergent series for these values.

Contribution

It introduces a generalized bivariate generating function identity for odd zeta values using the Markov-WZ method, extending previous formulas.

Findings

Derived a new identity for odd zeta values

Produced convergent series with ratio 2^{-10} for all ζ(2n+4m+3)

Unified previous formulas under a more general framework

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