An exact solution of the generalized exponential integral and its application to moment method formulations

The generalized exponential integral is one of the most fundamental integrals in antenna theory and for many years exact solutions to this integral have been sought. This paper considers an exact solution to the generalized exponential integral which is completely general and independent of the usual restrictions involving the wavelength, field point distance and dipole length is considered. The exact series representation presented converges rapidly in the induction and near-field regions of the antenna, and therefore provides an alternative to numerical integration. Two method of moments formulations are considered. They use the exact expression for the generalized exponential integral in the computation of the impedance matrix elements. It is demonstrated that, for very thin straight-wire antennas, an asymptotic expansion can be used to obtain a numerically convenient form of the generalized exponential integral