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The expansions of the electric and magnetic dyadic Green's functions are constructed in terms of the solenoidal Hansen vector wave functions in cylindrical coordinates. A static term is shown to arise in the course of conducting the radial spectral integral. This pole term has apparently not been identified in previously published expansions and is similar to recently identified static terms in Cartesian and spherical wave function expansions. The integration in the longitudinal spectral variable is considered, too, and forms which offer two alternative integration paths are constructed.