]> $$\begin{array}{rcl}\ln \left(\left|\Gamma \left(z\right)\right|\right)& =& \text{Δ}z\ln \left(\frac{\text{Δ}z+g+0.5}{e}\right)+\frac{1}{2}\ln \left(1+\frac{\text{Δ}z}{g+0.5}\right)+\ln \left(1+\sum _{k=0}^{N-1}\frac{\text{Δ}z{d}_k}{k\left(\text{Δ}z+k\right)}\right)\\ \text{Δ}z& =& 1-z\wedge d_k=\sqrt{\frac{g+0.5}{e}}\left(\frac{C_k}{e^g}\right)\end{array}$$