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:


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