A geometric analysis of the Maxwell field in a vicinity of a multipole particle and a new family of special functions

A method of solving Maxwell equations in a vicinity of a multipole particle (moving along ail arbitrary trajectory) is proposed. The method is based oil a geometric construction of a novel trajectory-adapted coordinate system, which simplifies considerably the equations. The solution is given in terms of a series, where a new family of special functions arises ill a natural way. Singular behaviour of the field near to the particle may be analyzed this Way Up to ail arbitrary order. Application to the self-interaction problems in classical electrodynamics is discussed. (C) 2009 Elsevier B.V. All rights reserved.