  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 a
geometric construction of a 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 in a natural way.
Singular behaviour of the field near to the particle may be analyzed this way
up to an arbitrary order. Application to the self-interaction problems in
classical electrodynamics is discussed.
