Harmonic integration of quasi polynomial potentials which are homogeneous in Euler terms

Electric and magnetic fields which are homogeneous in Euler terms are used to design the systems of charge particle optics with special properties. General theory of the harmonic functions which are homogeneous in Euler terms is an important instrument in this process. Quasi polynomial homogeneous potentials satisfying the Laplace equation and given in analytical form provide a sufficiently representative, but not complete, subset of 3D harmonic potentials which are homogeneous in Euler terms. The paper shows how, using harmonic integration, it is possible to extend the class of potentials that are given in analytical form, satisfy the Laplace equation and are homogeneous in Euler terms.