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 this integral which is completely general and independent of the usual restrictions involving the wavelength, field point distance, and dipole length. The generalized exponential integral has traditionally been evaluated numerically or by making certain convenient but restrictive assumptions. The exact series representation presented in this paper 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 which 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.