\begin{definition}[Definition:Hurwitz Zeta Function]
The '''Hurwitz zeta function''' is a generalization of the Riemann zeta function and is a special case of the Lerch Transcendent, defined for $\set {\map \Re s > 1, a \ne 0, -1, -2, \cdots}$ as the series: 
:$\ds \map \zeta {s, a} = \sum_{n \mathop = 0}^\infty \frac 1 {\paren {n + a}^s}$
{{ExtractTheorem|Extract that bit about Lerch Transcendent into a theorem page, as that line is too long and contains too much for {{ProofWiki}} presentational style}}
\end{definition}