An algorithm for generating Meixner’s series

Abstract

Divergence at edges is a fundamental property of solutions of Maxwell’s equations. About 30 years ago Josef Meixner proposed a method for analysis of the field behavior at edges. His recipe was to search for local solutions of Maxwell’s equations in the form of power series in the distance from the edge. The approach allows us to determine the order of singularity (at an edge) but the construction of the local solutions themselves has turned out to be very difficult. This paper introduces an approach, called the method of edge functions, that is a logical extension of the Meixner’s method. The approach not only recovers the Meixner’s results for the field behavior at edges, but also permits a complete specification of the local solutions.