An exact formulation for the vector potential of a cylindrical antenna with uniformly distributed current and arbitrary radius

An exact formulation is given for the vector potential and corresponding electric fields associated with a uniform current cylindrical dipole antenna of arbitrary radius. The exact expressions converge rapidly in the induction and near-field regions of the antenna. They are completely general and independent of the usual restrictions involving the wavelength, field point distance, dipole radius and length. The properties of these expressions allow them to be readily used for the efficient as well as accurate computational modeling of cylindrical wire antennas. An exact expression for the cylindrical wire kernel which is analytically as well as numerically convenient to work with is presented. It is demonstrated that the integral of the kernel can be expressed in terms of a series which involves a generalized exponential integral and higher-order associated integrals. Several methods for evaluating the generalized exponential integral are discussed, including some useful asymptotic expansions. A numerically stable forward recurrence relation for the higher-order associated integrals is also presented.>