Title: Une nouvelle démonstration du théorème d'André sur les E-fonctions au sens large
Abstract: We give a new proof of a theorem of Andre (2014) stating that every polynomial relation over $\overline{\mathbb{Q}}$ between values of a family of $E$-functions in the broad sense $(f_1, \dots, f_n)$ comes from a polynomial relation over $\overline{\mathbb{Q}}(z)$ between the $f_i(z)$. To this end, we prove a structure theorem on the $G$-operators in the broad sense : we begin by proving an analogue of Chudnovsky's theorem (1984) for the $G$-functions in the broad sense ; we then deduce from this that the minimal operator of a $G$-function in the broad sense is fuchsian. This makes possible to adapt to the case of the $E$-functions in the broad sense a proof of a theorem of Beukers (2006), which is an analogue of Andre's theorem in the case of the $E$-functions in the narrow sense.