\begin{definition}[Definition:Dirichlet Eta Function]
The '''Dirichlet $\eta$ (eta) function''' $\eta$ is the complex function defined on the half-plane $\map \Re s > 0$ as the series:
:$\ds \map \eta s = \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} n^{-s}$
\end{definition}