Generating Function Identities for $\zeta(2n+2), \zeta(2n+3)$ via the WZ Method
Generating Function Identities for $\zeta(2n+2), \zeta(2n+3)$ via the WZ Method
Using WZ-pairs we present simpler proofs of Koecher, Leshchiner and Bailey-Borwein-Bradley's identities for generating functions of the sequences $\{\zeta(2n+2)\}_{n\ge 0}$ and $\{\zeta(2n+3)\}_{n\ge 0}.$ By the same method, we give several new representations for these generating functions yielding faster convergent series for values of the Riemann zeta function.