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Some multi-set inclusions associated with shuffle convolutions and multiple zeta values. (English) Zbl 1016.11035
The authors develop a new method for obtaining combinatorial identities involving shuffle convolutions [see {\it D. Bowman} and {\it D. M. Bradley}, J. Comb. Theory, Ser. A 97, 43-61 (2002; Zbl 1021.11026)]. As an application, a new proof of the formula $\zeta (3,1,3,1,\ldots ,3,1)=2\pi^{4n}/(4n+2)!$, where $\{ 3,1\}$ is repeated $n$ times, is given. Some new identities for the multiple zeta function are also obtained.

11M41Other Dirichlet series and zeta functions
05A99Classical combinatorial problems
05E99Algebraic combinatorics
Full Text: DOI
[1] Borwein, J. M.; Bradley, D. M.; Broadhurst, D. J.: Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k. Electron. J. Combin. 4, No. 2, #R5 (1997) · Zbl 0884.40004
[2] Borwein, J. M.; Bradley, D. M.; Broadhurst, D. J.; Lisonĕk, P.: Special values of multiple polylogarithms. Trans. am. Math. soc. 353, No. 3, 907-941 (2000) · Zbl 1002.11093
[3] Borwein, J. M.; Bradley, D. M.; Broadhurst, D. J.; Lisonĕk, P.: Combinatorial aspects of multiple zeta values. Electron. J. Combin. 5, No. 1, #R38 (1998) · Zbl 0904.05012
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