The description of an electromagnetic beam for use in light scattering theories may be
carried out by using an expansion over vector spherical wave functions with expansion
coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to
evaluate these BSCs has been the use of localized approximations (with several existing
variants). We recently established that the use of any existing localized approximation is of
limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a …