File:ArcGamma.jpg

${\displaystyle z}$

The lines of constant ${\displaystyle u=\Re (\mathrm {ArcFactorial} (z)}$ and the lines of constant ${\displaystyle v=\Im (\mathrm {ArcFactorial} (z)}$ are drawn.
Levels ${\displaystyle u=1,2,3}$ are shown with thick black curves.
Levels ${\displaystyle u=0.2,0.4,0.6,0.8,1.2,1.4,1.6,1.8,2.2,2.4,2.6,2.8,3.2,3.4,3.6}$ are shown with thin blue curves.
Levels ${\displaystyle v=1,2,3}$ are shown with thick blue curves.
Level ${\displaystyle v=0}$ is shown with thick pink line.
Levels ${\displaystyle v=-1,-2,-3}$ are shown with thick red curves.
Intermediate levels of constant ${\displaystyle v}$ are shown with thin greel curves. The cutline of therange of holomorphizm is shown with dashed black line.

The same image can be considered also as plot of ArcGamma finction; in this case, the black curves corresponds to values of the real part 2,3,4.

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