Irrationality measures of values of E-functions

E-functions are a class of special functions introduced by Siegel in 1929; they include the exponential and Bessel functions. Very powerful qualitative results are known about their values, but their quantitative versions are more recent or still conjectural. In this lecture we shall focus on two recent results. First, values of E-functions at algebraic numbers are never Liouville : they are never extremely well approximated by rationals. Second, if an E-function with rational coefficients is evaluated at a rational number, a more precise result holds : if irrational, the value has exponent of irrationality 2, like a randomly chosen number. This is a joint work with Tanguy Rivoal, based mostly on results of Shidlovsky, Chudnovsky, André and Beukers.