Theorem on integration and differentiation of 3d electric and magnetic 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. This paper considers new proof of a fundamental theorem on representation of any harmonic and homogeneous in Euler terms scalar potential as a derivative of harmonic and homogeneous in Euler terms scalar potential of higher order. The said proof uses more weak assumptions about analytical properties of the scalar potential under consideration when usually. It is applicable to harmonic scalar potentials which are homogeneous in Euler terms and contains points with the violation of analytical properties of the function under consideration (in particular, singular points; in particular, at the origin of the coordinate system, which is typical for electric and magnetic fields).