On the general solution of the vector Helmholtz equation in cylindrical polar coordinates

The general solution to the vector Helmholtz equation in cylindrical polar coordinates is derived by choosing combinations of components for which the equations do separate. A recent approximate solution form for the azimuthal component assumed by J. C. Piquette, ‘‘Spherical wave scattering by an elastic solid cylinder of infinite length’’ [J. Acoust. Soc. Am. 79, 1248–1259 (1986)], may with slight modification accordingly be rendered exact. The radial component need not be assumed to be approximated by zero; the corresponding actual exact solution is displayed.