# Definition:Dirichlet Beta Function

## Definition

The Dirichlet beta function $\beta$ is the complex function defined on the half-plane $\map \Re s > 0$ by the series:

$\displaystyle \map \beta s = \sum_{n \mathop = 0}^\infty \frac {\paren {-1}^n} {\paren {2 n + 1}^s}$

## Also see

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

## Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.