  We calculate the one-particle density of states for the Mott-Hubbard
insulating phase of the Hubbard model on a Bethe lattice in the limit of
infinite coordination number. We employ the Kato-Takahashi perturbation theory
around the strong-coupling limit to derive the Green function. We show that the
Green function for the lower Hubbard band can be expressed in terms of
polynomials in the bare hole-hopping operator. We check our technique against
the exact solution of the Falicov-Kimball model and give explicit results up to
and including second order in the inverse Hubbard interaction. Our results
provide a stringent test for analytical and numerical investigations of the
Mott-Hubbard insulator and the Mott-Hubbard transition within the dynamical
mean-field theory. We find that the Hubbard-III approximation is not
satisfactory beyond lowest order, but the local-moment approach provides a very
good description of the Mott-Hubbard insulator at strong coupling.
