Euler gamma function (reviewed)

The (Euler) gamma function $\Gamma(z)$ is defined by the integral $$ \Gamma(z) = \int_0^{ \infty } e^{-t} t^{z} \frac{dt}{t} $$ for Re$(z) > 0$. It satisfies the functional equation $$ \Gamma(z+1) = z \Gamma(z), $$ and can thus be continued into a meromorphic function on the complex plane, whose poles are at the non-positive integers $\{0,-1,-2,\ldots\}$.