  The Mott-Hubbard transition in the half-filled Hubbard model is studied
analytically for the paramagnetic ground state and the classical N\'{e}el
state. The single-particle density of states is obtained by calculating the
Green's function represented by the infinite continued fraction. The
paramagnetic solution shows that the Mott-Hubbard transition is signaled by
both collapsing Hubbard bands and appearing $\delta$-function peak at midgap,
and the transition is second order at the ground state. We also provide
specific heats in metallic regime to demonstrate that our results recover those
of infinite dimension.
