An analytic representation for the potential of a uniform elliptic cone

In view of the fact that various gravitating and charged bodies may have singular points on their surface, the problem of the effect of these singularities in the mass distribution on the behavior of potential arises. The analytic representation for gravitational and electrostatic potentials of a uniform elliptic cone in terms of ordinary integrals is derived. Generally, these integrals are somewhat more complicated than the elliptic ones; however, they reduce to elementary functions in the case of a circular cone. The arbitrariness in the way of truncating a cone manifests itself in the possibility of adding various harmonic polynomials. However, the singularity of potential in the vicinity of the vertex of a cone is of an objective and unique character.