This paper discusses the problem of light scattering by an arbitrary axisymmetric particle in the electrostatic approximation. Since the wave number is assumed to equal zero, instead of Maxwell's equations in the framework of the method of separation of variables, Laplace's equation for scalar potentials or an equivalent integral equation was solved in the framework of the method of expanded boundary conditions, which in essence is a version of the separation-of-variables method. These approaches made it possible to find rigorous solutions of the problem for axisymmetric particles. On the assumption of a constant field inside the particle, an approximate solution that coincides with the exact solution in the case of ellipsoids was also constructed. Numerical calculations showed that the Rayleigh approximation subsequently constructed works well in a wide range of values of the parameters of the problem and gives satisfactory agreement with the results of calculations by the rigorous methods of scattering theory.