\[\frac{1}{2\pi}\int_{-\infty}^{\infty}\Gamma\left(a+it\right)\Gamma\left(b+it%
\right)\Gamma\left(c-it\right)\Gamma\left(d-it\right)\,\mathrm{d}t=\frac{%
\Gamma\left(a+c\right)\Gamma\left(a+d\right)\Gamma\left(b+c\right)\Gamma\left(%
b+d\right)}{\Gamma\left(a+b+c+d\right)},\]