Some multi-set inclusions associated with shuffle convolutions and multiple zeta values
The authors develop a new method for obtaining combinatorial identities involving shuffle convolutions [see \textit{D. Bowman} and \textit{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.
scientific article; zbMATH DE number 1895804
scientific article