Light scattering problem solutions using the field expansions in wave functions: convergence and the Rayleigh hypothesis

The problem of light scattering by a non-spherical obstacle is most often solved today by the SVM, EBCM and PMM methods applying the field expansions in terms of wave functions. The methods are based on quite different formulations of the problem and hence were earlier discussed separately. We demonstrate tight relations of the methods and present some results of our recent theoretical and numerical studies of the methods that illustrate their similarity and differences.