Solution to Carson 's integrals through power series

The problem ofelectromagnetic waves propagation inoverhead transmissionlines has apparently not been solved in a sound manner yet. While the problemdoes not have anexact analyticalsolutionwhen considering the presence of the actual surface of theearth, its approximate solutionintroducingtheoreticalsimplificationsis of formidable practical interest. Using quasi-static approximations Carson obtained integral equations to calculate the electromagnetic field due to a horizontal current carrying wire which is above a lossy ground plane. Carsonhimselfproposedthe first solutionto theseexpressions using power series expansions which does not possess uniform convergence andsincethen there have beenefforts toget a bettersolution. In this sense two clear approaches have been essentially followed. The first one consists on modifying the integrand in such a way that an analytic solution can be obtained. The second one is based on using numerical integration schemes.