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

Keywords:

multiple zeta (star) values
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