  A closed form expression for the ground state energy density of the general
extensive many-body problem is given in terms of the Lanczos tri-diagonal form
of the Hamiltonian. Given the general expressions of the diagonal and
off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and
$\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in
terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is
the size of the system). By application of theorems on the zeros of orthogonal
polynomials we find the ground-state energy density in the bulk limit to be
given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) -
2\,\beta(z)\right]$.
