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A partial eigenfunction expansion of the electric-type dyadic Green's function used in aperture-coupled waveguide problems is discussed in connection with the traditional Green's function expansion in terms of the waveguide modes. Based on the principles of distributions, the delta-function term is extracted from a double series, resulting in the complete representation of the Green's function in the source region. This, in turn, is related to inclusion of the term with zero indices in the computation of the double-series expansion, even though it does not correspond to any waveguide mode. The effect of exclusion of this term from the series, and controversies over published results in the analysis of slotted-waveguide couplers and radiators, are illustrated.