A general analytical formula describing the transfer function between the input and output of an arbitrary rectangular multimode interference (MMI) coupler has been derived using the elliptic theta function ϑ(x', z'). This formula provides the positions, amplitudes and relative phases of all the self-images of a given source. It is shown how the transfer function can be used as a propagation matrix for any rectangular NxM MMI. Specific simplified solutions for NxN, symmetric and paired MMIs are also derived from the general formula.