We define, for all $x \in \mathbb{R}^{+*}$, $$\Gamma(x) = \int_0^{+\infty} t^{x-1} \mathrm{e}^{-t} \, \mathrm{d}t$$ Determine the value of $\Gamma(n)$, for $n \in \mathbb{N}^*$.
We define, for all $x \in \mathbb{R}^{+*}$,
$$\Gamma(x) = \int_0^{+\infty} t^{x-1} \mathrm{e}^{-t} \, \mathrm{d}t$$
Determine the value of $\Gamma(n)$, for $n \in \mathbb{N}^*$.