Given three real numbers $a, b$ and $c$ with $c \in D$, the Gauss hypergeometric function is defined by
$$F_{a,b,c}(x) = \sum_{n=0}^{+\infty} \frac{[a]_n [b]_n}{[c]_n} \frac{x^n}{n!}$$
Express the function
$$x \mapsto \begin{cases} \frac{\ln(1+x)}{x} & \text{if } x \in ]-1,1[ \setminus \{0\} \\ 1 & \text{if } x = 0 \end{cases}$$
using a Gauss hypergeometric function.