Application of generalized spherical functions in the spherically symmetric dynamo problem (Q1571301)

The author develops the theory of generalized spherical functions representing the exact solutions to the spherically symmetric dynamo problem for an anisotropic conducting medium. In the limiting case of an isotropic medium, these functions reduce to the conventional spherical functions, which can be used as a basis for expanding a solution to the Laplace equation in a ball. In particular, an efficient method based on generalized spherical functions can be constructed for solving certain problems in the dynamics of artificial plasma objects in the near-Earth space.