Logarithmic terms in fields near the edge of a dielectric wedge

The author follows the method proposed by G.I. Makarov and A.V. Osipov (1986) and verifies that the Meixner solution for the field in the presence of an infinite dielectric wedge is valid for wedge angles that are not rational multiples of pi . For angles that are rational multiples of pi the author determines what additional terms containing powers of log rho are needed in the expansion. The form of the expansion differs for different angles, and there are additional arbitrary constants in the solution. The longitudinal field behaves like a constant due to the t=0 contribution. The transverse fields are expected to be singular and behave as predicted by Meixner. Numerical experiments only partially verify this conclusion. The expansion proposed by Osipov and Makarov eliminates the difficulty with Meixner´s series.<>