The symmetry group and harmonic potentials of a generalized multipole

The relation between the M function for a generalized multipole and the pure mathematical M function is discussed. The concept of rotation sense has been replaced by the clearer and more general concept of screw sense. The influence of the infinitesimal orders of harmonic potentials on aberrations in connection with the constraints of the symmetry group of a GM are discussed. A simple, unified and powerful method to determine the constraint relations among the harmonic potentials of a generalized multipole or ordinary multipole is given and rigorously proved.