  We develop an analytical expression for the self-energy of the
infinite-dimensional Hubbard model that is correct in a number of different
limits. The approach represents a generalization of the iterative perturbation
theory to arbitrary fillings. In the weak-coupling regime perturbation theory
to second order in the interaction U is recovered. The theory is exact in the
atomic limit. The high-energy behavior of the self-energy up to order (1/E)**2
and thereby the first four moments of the spectral density are reproduced
correctly. Referring to a standard strong-coupling moment method, we analyze
the limit of strong U. Different modifications of the approach are discussed
and tested by comparing with the results of an exact diagonalization study.
