Equivalence of the Rayleigh solution and the extended-boundary-condition solution for scattering problems

Methods based on the Rayleigh hypothesis (e.g. the point-matching method) for numerically solving wave-diffraction problems are shown to be equivalent to the exact extended-boundary-condition method. It is concluded that the Rayleigh hypothesis is exact, although, in general, it is necessary to interpret it in the generalised function sense.