The paper deals with the application of the spherical-harmonics method to systems with complete cylindrical symmetry, that is, to systems invariant under rotation around and translation parallel to an axis. Closed-form expressions are given in an arbitrary order of approximation both for the spherical-harmonics moments in terms of the constants of integration and, conversely, for the constants of integration in terms of the spherical-harmonics moments. This removes the need for numerical inversion of matrices and simplifies the treatment of multilayer problems.