  We consider the Hubbard model on the infinite-dimensional Bethe lattice and
construct a systematic series of self-consistent approximations to the
one-particle Green's function, $G^{(n)}(\omega),\ n=2,3,\dots\ $ . The first
$n-1$ equations of motion are exactly fullfilled by $G^{(n)}(\omega)$ and the
$n$'th equation of motion is decoupled following a simple set of decoupling
rules. $G^{(2)}(\omega)$ corresponds to the Hubbard-III approximation. We
present analytic and numerical results for the Mott-Hubbard transition at half
filling for $n=2,3,4$.
