  We have found an exact formula expressing a general correlation function
containing both products and ratios of characteristic polynomials of random
Hermitian matrices. The answer is given in the form of a determinant. An
essential difference from the previously studied correlation functions (of
products only) is the appearance of non-polynomial functions along with the
orthogonal polynomials. These non-polynomial functions are the Cauchy
transforms of the orthogonal polynomials. The result is valid for any ensemble
of beta=2 symmetry class and generalizes recent asymptotic formulae obtained
for GUE and its chiral counterpart by different methods..
