On applicability of the extended boundary condition method with the spheroidal basis

The problem of light scattering by small particles is commonly solved today by the extended boundary condition method (EBCM) that uses expansions of the fields in terms of wave functions. The method is known to have a limited range of applicability. We analytically study the method in the case when spheroidal functions are applied. We find the conditions under which such a version of the EBCM method is mathematically correct and can be used for calculations in the far-field zone.