Algebraic description of the maxwell field singularity in a neighbourhood of a multipole particle

An algebraic procedure is proposed, which enables us to calculate (up to an arbitrary order) the singular part of the Maxwell field in a neighbourhood of an (arbitrarily moving) multipole particle. The procedure may also be used for particles carrying magnetic moment. An algorithm based on the MAPLE V system for symbolic calculus was used to calculate the field of a moving dipole up to terms proportional to r.