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{\bf Kh.~Hessami Pilehrood and T.~Hessami Pilehrood}
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{\bf Generating Function Identities for $\zeta(2n+2), \zeta(2n+3)$ via the WZ Method}
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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.



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