Definition:Hurwitz Zeta Function

Definition
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:


 * $\ds \map \zeta {s, a} = \sum_{n \mathop = 0}^\infty \frac 1 {\paren {n + a}^s}$