Gabriel Lepetit

Siegel's $E$ and $G$-functions are classes of special functions
including many classical functions, such as polylogarithms and
hypergeometric functions. They have the crucial property to be solutions
of linear differential equations with polynomial coefficients.

In this talk, we begin by presenting the known irrationality and
transcendence results on the values of $E$ and $G$-functions. Then we
will interest ourselves in their differential properties.