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An interface for evaluation of Euler sums.

Definitions:

The EZ-Face (Euler Zeta interface) is primarily intended for evaluating the Euler sums

\begin{displaymath} \zeta(s_1,\ldots,s_k):= \sum_{n_1\gt\ldots\gt n_k\gt} \prod_{j=1}^k { {{a_j}^{n_j}}\over {n_j^{\vert s_j\vert}} },\end{displaymath}

where all sj are non-zero integers and

\begin{displaymath} a_j:=\mbox{sign}(s_j)\in\{-1,1\} \ \ \ \mbox{for\ }j=1,\ldots,k.\end{displaymath}

A non-alternating Euler sum (i.e., all aj=1) is called a multiple zeta value (MZV).


Aditionally, for non-negative integers $s_1,\ldots,s_k$ and $p\ge 1$we define

\begin{displaymath} \zeta_p(s_1,\ldots,s_k) :=\sum_{n_1\gt\ldots\gt n_k\gt} p^{-n_1}\prod_{j=1}^k n_j^{-s_j},\end{displaymath}

which reduces to an MZV when p=1.
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