Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin

We obtain analytic expressions for the third-order corrections due to the strong interaction Coulomb potential to the S-wave Green function, energy levels and wave functions at the origin for arbitrary principal quantum number n. Together with the known non-Coulomb correction this results in the complete spectrum of S-states up to order αs5. The numerical impact of these corrections on the upsilon spectrum and the top quark pair production cross section near threshold is estimated.