Geodesic
Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the WZ method
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl arXiv
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.
DOI : 10.37236/759
Classification : 11M06, 33C20, 33F10
Mots-clés : Riemann zeta function, generating function, Markov--Wilf--Zeilberger method, Markov--WZ pair 
Kh. Hessami Pilehrood; T. Hessami Pilehrood. Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the WZ method. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/759
@article{10_37236_759,
     author = {Kh. Hessami Pilehrood and T. Hessami Pilehrood},
     title = {Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the {WZ} method},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/759},
     zbl = {1219.11121},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/759/}
}
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