Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the WZ method
The electronic journal of combinatorics, Tome 15 (2008)
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
Mots-clés : Riemann zeta function, generating function, Markov--Wilf--Zeilberger method, Markov--WZ pair
@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/}
}
TY - JOUR AU - Kh. Hessami Pilehrood AU - T. Hessami Pilehrood TI - Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the WZ method JO - The electronic journal of combinatorics PY - 2008 VL - 15 UR - http://geodesic.mathdoc.fr/articles/10.37236/759/ DO - 10.37236/759 ID - 10_37236_759 ER -
%0 Journal Article %A Kh. Hessami Pilehrood %A T. Hessami Pilehrood %T Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the WZ method %J The electronic journal of combinatorics %D 2008 %V 15 %U http://geodesic.mathdoc.fr/articles/10.37236/759/ %R 10.37236/759 %F 10_37236_759
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
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