\begin{definition}[Definition:Polylogarithm]
The '''polylogarithm''' is a generalization of the Riemann Zeta Function and is a special case of the Lerch Transcendent, defined for $\set {z \in \C: 0 \le z < 1}$ as the series:
:$\ds \Li_s \paren z = \sum_{n \mathop = 1}^\infty \frac {z^n} {n^s}$
\end{definition}