# 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

• Results about Dirichlet $\eta$ function can be found here.

## Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.