Calculation of the one- and two-loop lamb shift for arbitrary excited hydrogenic states

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Z alpha)(6)] and for the two-loop Lamb shift [of order alpha(2)(Z alpha)(6)] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Delta(n)=n(3)Delta E(nS)-Delta E(1S). We present numerical results for one-loop and two-loop corrections for excited S, P, and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty of order 0.1 kHz.