On a new cylindrical harmonic representation for spherical waves

An exact series representation is presented for integrals whose integrands are products of cosine and spherical wave functions, where the argument of the cosine term can be any integral multiple n of the azimuth angle phi. Th is series expansion will be shown to have the following form: [GRAPHICS] It is demonstrated that in the special cases n = 0 and n = 1, this series r epresentation corresponds to existing expressions for the cylindrical wire kernel and the uniform current circular loop vector potential, respectively . A new series representation for spherical waves in terms of cylindrical h armonics is then derived using this general series representation. Finally, a closed-form far-field approximation is developed and is shown to reduce to existing expressions for the cylindrical wire kernel and the uniform cur rent loop vector potential as special cases.