Dirichlet eta-function

Definition

The Dirichlet eta-function is defined as the meromorphic function given by the following Dirichlet series:

$\eta (s)={\sum }_{n\in \mathbb{N}}\frac{(-1{)}^{n-1}}{n^s}$.

It can also be defined in terms of the Riemann zeta-function as:

$\eta (s)=(1-2^{1-s})\zeta (s)$.

Relation with other functions

• Riemann zeta-function