Two-loop self-energy for the ground state of medium- Z hydrogenlike ions

The two-loop self-energy correction to the ground-state Lamb shift is calculated for hydrogenlike ions with the nuclear charge $Z=10--30$ without any expansion in the binding field of the nucleus. A calculational technique is reported for treatment of Feynman diagrams in the mixed coordinate-momentum representation, which yields significant improvement in numerical accuracy as compared to previous results. An extrapolation of the all-order numerical data yields a result for the higher-order remainder function for hydrogen. The previously reported disagreement between the all-order and the perturbative approaches is reduced to the marginal agreement.