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A method of solving Maxwell equations in a vicinity of a multipole particle(moving along an arbitrary trajectory) is proposed. The method is based on ageometric construction of a trajectory-adapted coordinate system, whichsimplifies considerably the equations. The solution is given in terms of aseries, where a new family of special functions arises in a natural way.Singular behaviour of the field near to the particle may be analyzed this wayup to an arbitrary order. Application to the self-interaction problems inclassical electrodynamics is discussed.

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