$\Gamma(z)$

\(\Gamma(z) = \int_{0}^{\infty} t^{z-1}e^{-t} dt\)

for \(Re(z) > 0\)

if \(Re(n), n \in N^+\), we have

\(\Gamma(n) = (n-1)! = (n-1)(n-2)!\),

\(\Gamma(n+1) = n \Gamma(n)\)