File:Factorialz.jpg

${\displaystyle z}$

the lines of constant ${\displaystyle u=\Re (z!)}$ and the lines of constant ${\displaystyle v=\Im (z!)}$ are shown. The levels ${\displaystyle u=-24,-20,-16,-12,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,12,16,20,24}$ are drown with thick black lines. some of intermediate levels ${\displaystyle u=}$const are shown with thin blue lines for positive values and with thin red lines for negative values.
The levels ${\displaystyle v=-24,-20,-16,-12,-8,-7,-6,-5,-4,-3,-2,-1}$ are shown with thick red lines.
The level ${\displaystyle v=0}$ is shown with thick pink lines.<be> The levels ${\displaystyle v=1,2,3,4,5,6,7,8,12,16,20,24}$ are drown with thick blue lines. some of intermediate levels ${\displaystyle v=}$const are shown with thin green lines.
The dashed blue line shows the level ${\displaystyle u=\mu _{0}\approx 0.88560319441}$ and corresponds to the value of the principal local minimum of the factorial of the real argument.

The dashed red line shows the level ${\displaystyle u=\mu _{1}\approx -3.544643611}$ and corresponds to the value of the first local maximum of the factorial of the real argument.

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