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# Gamma function

The Gamma function ${\displaystyle \Gamma (s)}$ extends the factorial function to all complex numbers.
${\displaystyle \Gamma (s)=\int _{0}^{1}(\log({\frac {1}{t}}))^{s-1}dt}$
For a positive integer ${\displaystyle n}$, this works out to ${\displaystyle \Gamma (n)=(n-1)!}$. For example, ${\displaystyle \Gamma (7)=720}$. Here's a complex number example: ${\displaystyle \Gamma (\pi +i)\approx 1.0302984+1.6026i}$.