Integral Representation of Dirichlet Eta Function in terms of Gamma Function

Theorem

 * $\displaystyle \map \eta s = \frac 1 {\map \Gamma s} \int_0^\infty \frac {x^{s - 1} } {e^x + 1} \rd x$

where:
 * $s$ is a complex number with $\map \Re s > 0$
 * $\eta$ denotes the Dirichlet eta function
 * $\Gamma$ denotes the Gamma function.