\begin{definition}[Definition:Lerch Transcendent]
The '''Lerch Transcendent''', is a generalization of the Hurwitz Zeta Function and of the Polylogarithm defined for $\set {z \in \C: 0 \le z < 1, a \ne 0, -1, -2, \cdots }$ as the series:
:$\ds \map \Phi {z, s, a} = \sum_{n \mathop = 0}^\infty \frac {z^n} {\paren {n + a}^s}$
{{NamedforDef|Mathias Lerch|cat = Lerch}}
\end{definition}