Communications in Number Theory and Physics

Volume 2 (2008)

Number 2

Zeta stars

Pages: 325 – 347

DOI: http://dx.doi.org/10.4310/CNTP.2008.v2.n2.a2

Authors

Yasuo Ohno (Kinki University, Osaka, Japan)

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

Abstract

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 $\sum_{l=2}^{n-1}\zeta(l,\breakn-l)=\zeta(n)$ ($n\ge3$).

Full Text (PDF format)