\[\frac{1}{4\pi}\int_{-\infty}^{\infty}\frac{\prod_{k=1}^{4}\Gamma\left(a_{k}+it%
\right)\Gamma\left(a_{k}-it\right)}{\Gamma\left(2it\right)\Gamma\left(-2it%
\right)}\,\mathrm{d}t=\frac{\prod_{1\leq j<k\leq 4}\Gamma\left(a_{j}+a_{k}%
\right)}{\Gamma\left(a_{1}+a_{2}+a_{3}+a_{4}\right)},\]