Analysis of the general Whittaker’ formula for 3D electric and magnetic potentials homogeneous in Euler terms

Electric and magnetic fields which are homogeneous in Euler terms are a useful instrument to design the systems of charge particle optics. The similarity principle for charged particle trajectories in these fields which was realized by Yu.K. Golikov for the first time enables to create spectrographic charge particle optical systems in a more systematic and intelligence way by using the fields which are homogeneous in Euler terms. This paper considers the Whittaker’ formulas for 3D Laplace potentials which are homogeneous in Euler terms. This paper is the continuation of the cycle of publications devoted to the study of the properties of harmonic functions homogeneous in Euler terms and its applications to create effective electron and ion optical systems.