Generating function identities for $ζ(2n+2), ζ(2n+3)$ via the WZ method

Details Generating function identities for $ζ(2n+2), ζ(2n+3)$ via the WZ method Generating function identities for $ζ(2n+2), ζ(2n+3)$ via the WZ method

2008-01-10

arxiv.org/abs/0801.1591v2

Mathematics

Number Theory

7 pages

Scientific paper

Using the WZ method we present simpler proofs of Koecher's, Leshchiner's and
Bailey-Borwein-Bradley's identities for generating functions of the sequences
$\{\zeta(2n+2)\}_{n\ge 0}, \{\zeta(2n+3)\}_{n\ge 0}.$ 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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