Generating functions with graded variables are mainly used for the description of disordered systems. Instead of averaging over many random samples, the averaging procedure is performed only once with a generating function containing anticommuting variables. An approach is described for the calculation of correlation functions by transfer matrix methods including the aspect of anticommuting variables. The transfer matrix of the generating function of a disordered many body system is constructed in coherent state representation and transformed to a differential eigenvalue equation. According to the presence of anticommuting numbers, this general eigenvalue equation separates into sets of differential eigenvalue systems of commuting variables. These characteristic eigenvalue systems are reduced with operators and their commutation relations to an ordinary Sturm Liouville eigenvalue problem whose lowest eigenvalues contain the information about the averaged, asymptotic critical values of the correlation function. The eigensolutions for the U(N) symmetry preserving problem can be obtained from a recursion process for eigenstates with an arbitrary number M of anticommuting pairs χ*χ, (1 ≤ j ≤ M) which is proved by induction. The given approach, avoiding statistical averaging techniques, can be generalized to problems with U(N) symmetry breaking terms.