2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184566We 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..published version, with a few misprints correctedMathematical PhysicsCondensed MatterHigh Energy Physics - TheoryExactly Solvable and Integrable Systemstext