Generating Function Identities for ζ(2n+2), ζ(2n+3) via the WZ Method - Pilehrood, Kh. Hessami; Pilehrood, T. Hessami (The Electronic Journal of Combinatorics, 2008)
Using WZ-pairs we present simpler proofs of Koecher, Leshchiner and Bailey-Borwein-Bradley’s identities for generating functions of the sequences {ζ(2n+2)}_n0 and {ζ(2n+3)}_n0. By the same method, we give several new representations for these generating functions yielding faster convergent series for values of the Riemann zeta function.