I revisit the 1-loop self-energy of an electron of mass m in a strong, constant and uniform external magnetic field B. First, I show, after Tsai [1], how, for an electron in the lowest Landau level, Schwinger’s techniques [2] explained by Dittrich and Reuter [3] lead to the same integral deduced by Demeur [4] and used later by Jancovici [5]. Then, I calculate the Demeur-Jancovici integral in th...