Communications in Number Theory and Physics

Volume 2 (2008)

Number 2

Zeta stars

Pages: 325 – 347



Yasuo Ohno (Kinki University, Osaka, Japan)

Wadim Zudilin (Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia)


We present two new families of identities for the multiple zeta(star) values: The first one generalizes the formula$\zetas(\{2\}_n,1)=2\zeta(2n+\nobreak1)$, where $\{2\}_n$ denotes the$n$-tuple $(2,2,\ldots,2)$, while the second family is a weightedanalogue of Euler’s formula $\sum_{l=2}^{n-1}\zeta(l,\breakn-l)=\zeta(n)$ ($n\ge3$).

Published 1 January 2008