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 in tegrals in antenna theory and for many years exact solutions to this i ntegral have been sought. This paper considers an exact solution to th is integral which is completely general and independent of the usual r estrictions involving the wavelength, field point distance, and dipole length. The generalized exponential integral has traditionally been e valuated numerically or by making certain convenient but restrictive a ssumptions. The exact series representation presented in this paper co nverges rapidly in the induction and near-field regions of the antenna and therefore provides an alternative to numerical integration. Two m ethod of moments formulations are considered which use the exact expre ssion for the generalized exponential integral in the computation of t he impedance matrix elements. It is demonstrated that, for very thin s traight-wire antennas, an asymptotic expansion can be used to obtain a numerically convenient form of the generalized exponential integral.