Transcendance et irrationalité, 1–20. Journée annuelle 2012 de la SMF.  

Abstract: 

In this survey we present the parameterized Galois theory of difference equations, as introduced by Hardouin-Singer. The purpose of this theory is to give a systematic approach to differential transcendence, also called hypertranscendence. As an example of the applications, we explain the Galoisian proof of Hölder's theorem on the differential transcendence of the Gamma function.

ArXiv:1404.3611