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Zeta stars. (English) Zbl 1228.11132
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
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