Solution of the electrostatic problem for a core-mantle particle with non-confocal spheroidal boundaries of the mantle

Problem of light scattering by a layered particle with non-confocal spheroidal boundaries of the layers is typically considered in a framework of numerical methods. We suggest a rigorous method of solving this problem and apply it to a similar (but more simple) electrostatic problem. We discuss advantages of the method and demonstrate that it provides new approximations useful for a fast solution of the problem.