  In this article, a model of random hermitian matrices is considered, in which
the measure $\exp(-S)$ contains a general U(N)-invariant potential and an
external source term: $S=N\tr(V(M)+MA)$. The generalization of known
determinant formulae leads to compact expressions for the correlation functions
of the energy levels. These expressions, exact at finite $N$, are potentially
useful for asymptotic analysis.
