\[\Gamma\left(\tfrac{1}{2}+\mathrm{i}y\right)\Gamma\left(\tfrac{1}{2}-\mathrm{i}%
y\right)=\left|\Gamma\left(\tfrac{1}{2}+\mathrm{i}y\right)\right|^{2}=\frac{%
\pi}{\cosh\left(\pi y\right)},\]