\[\operatorname{Ln}\Gamma\left(z\right)=\left(z-\tfrac{1}{2}\right)\ln z-z+%
\tfrac{1}{2}\ln\left(2\pi\right)-\frac{z}{\pi}\int_{0}^{\infty}\frac{\ln\left(%
1-{\mathrm{e}}^{-2\pi t}\right)}{t^{2}+z^{2}}\,\mathrm{d}t,\]