  We solve the Bethe-Salpeter equation for hydrogenic bound states by choosing
an appropriate interaction kernel $K_c$. We want to use our solution to
calculate up to a higher order the hydrogen Lamb-shift, and as a first
application we present up to order $\left(\aa / \pi\right)(\za)^7$ the
contribution of the lowest order self-energy graph, calculated {\it exactly}.
The basic formalism is a natural extension to the hydrogenic bound states of
the one previously presented by R. Barbieri and E. Remiddi and used in the case
of positronium.
