Definition:Dirichlet Eta Function

Definition
The Dirichlet $\eta$ (eta) function $\eta$ is the complex function defined on the half-plane $\map \Re s > 0$ as the series:


 * $\displaystyle \map \eta s = \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} n^{-s}$

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

Also see

 * Definition:Riemann Zeta Function
 * Riemann Zeta Function in terms of Dirichlet Eta Function

Generalizations

 * Definition:Dirichlet Series