The "spherical-harmonics" problem is investigated for a cone of arbitrary cross section. The analysis shows that two basic singularities must be considered: 1) the electric singularity, in which

becomes infinite like

near the tip of the cone, 2) the magnetic singularity, in which

becomes infinite like

. Numerical results, in particular concerning

and

, are given for: 1) the elliptic cone and its limiting case the sector, 2) the pyramidal corner.