On a new cylindrical harmonic representation for spherical waves

An exact series representation was derived for integrals whose integrands are products of cosine and spherical wave functions. For purposes of illustration, the kernel integral for a cylindrical dipole and the vector potential for a uniform current circular loop were evaluated. Further, the representation was used to develop a new and useful series expansion for a spherical wave in terms of cylindrical harmonics. A general closed-form far-field approximation was also established and shown to reduce to the known results for the special cases of the cylindrical wire kernel and the uniform current loop vector potential.