Zeta stars. (English) Zbl 1228.11132

Ohno, Yasuo; Zudilin, Wadim

Commun. Number Theory Phys. 2, No. 2, 325-347 (2008).

Summary: We present two new families of identities for the multiple zeta (star) values: The first one generalizes the formula \(\zeta^*(\{2\}_n, 1) = 2\zeta(2n + 1)\), where \(\{2\}_n\) denotes the \(n\)-tuple \((2, 2, \dots, 2)\), while the second family is a weighted analogue of Euler’s formula \(\sum_{l=2}^{n-1} \zeta(l, n-l) = \zeta(n)\) \((n\geq 3)\).

MSC:

11M32	Multiple Dirichlet series and zeta functions and multizeta values
33B30	Higher logarithm functions

Keywords:

multiple zeta (star) values