Barnes' Lemma

If a Contour in the Complex Plane is curved such that it separates the increasing and decreasing sequences of Poles, then

$${1\over 2\pi i} \int_{-i\infty}^{i\infty} \Gamma(\alpha+s)\G... ...)\Gamma(\beta+\delta)\over\Gamma(\alpha+\beta+\gamma+\delta)},$$

where $\Gamma(z)$ is the Gamma Function.