Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation RAS, Troitsk, Moscow region, Russia

E-mail: dumin@center.izmiran.troitsk.ru

We give a brief description of solving the dynamo-effect problem in an expanding plasma ball by using the generalized spherical functions, which represent generalization of the well-known Legendre polynomials and were introduced in our previous studies. Examples of particular analytic solutions for the simplest boundary conditions are presented.