The Pochhammer symbol is defined, for any real number $a$ and any natural integer $n$, by
$$[a]_n = \begin{cases} 1 & \text{if } n = 0 \\ a(a+1)\cdots(a+n-1) = \prod_{k=0}^{n-1}(a+k) & \text{otherwise} \end{cases}$$
Let $n \in \mathbb{N}$. Give an expression of $[a]_n$
\begin{itemize}
\item using factorials when $a \in \mathbb{N}^*$;
\item using two values of the function $\Gamma$, when $a \in D$.
\end{itemize}