Definition:Dirichlet Eta Function

Definition
The Dirichlet $\eta$ (eta) function $\eta: \C \to \C$ is a complex function defined as:


 * $\displaystyle \eta \left({s}\right) := \sum_{n \mathop = 1}^\infty \left({-1}\right)^{n - 1} n^{-s}$ for $\operatorname{Re} \left({s}\right) > 0$.

The Dirichlet $\eta$ function is an example of a Dirichlet series.

Also known as
It is also known as the alternating $\zeta$ (zeta) function.

Also see

 * Definition:Riemann Zeta Function