File:Factorial05.jpg

${\displaystyle ~\rho ~}$ and phase ${\displaystyle ~\varphi ~}$ of !actorial ${\displaystyle f=\rho \exp({\rm {i}}\varphi )=(x+{\rm {i}}y)!=\Gamma (x+{\rm {i}}y+1)}$ in the complex ${\displaystyle x+{\rm {i}}y}$ plane. Several levels of constant modulus (amplitude) ${\displaystyle \rho ={\rm {const}}}$ and constant phase ${\displaystyle \varphi ={\rm {const}}}$ are shown. Set ${\displaystyle ~f<0~}$ is shown with scratched line. The grid covers range ${\displaystyle ~-3\leq x\leq 3~}$, ${\displaystyle ~-2\leq y\leq 2~}$