Dirichlet Beta Function in terms of Hurwitz Zeta Function

Theorem

 * $\displaystyle \map \beta s = \frac 1 {4^s} \paren {\map \zeta {s, \frac 1 4} - \map \zeta {s, \frac 3 4} }$

where:
 * $\beta$ is the Dirichlet beta function
 * $\zeta$ is the Hurwitz zeta function
 * $s$ is a complex number.