Electron self-energy in QED at two loops revisited

We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the iterated integrals, we consider the four cases p(2) = 0, p(2) = m(2), p(2) = 9m(2) and p(2) = infinity. The iterated integrals have q-expansions, which can be used for the numerical evaluation. We show that a truncation of the q-series to order O(q(30)) gives numerically, for the finite part of the self-energy, a relative precision better than 10(-20) for all real values p(2)/m(2).