On the calculation of some definite integrals in antenna theory

Summary The mutual radiation resistance of two identical linear antennae is usually calculated by using the e.m.f. method. However, in a recent paper it has been demonstrated by the author that sometimes a simple expression for the mutual radiation resistance of two antennae, derived on the basis of the Poynting vector method, may be used with advantage. In most cases, however, the results obtained by using this modified Poynting vector method contain integrals which are difficult to express by known functions. By equating the expression for the mutual radiation resistance derived on the basis of the Poynting vector method with that obtained by the e.m.f. method we may therefore obtain a useful mathematical formula expressing a definite integral by known functions. This heuristic procedure for generating formulae for some definite integrals has been used in several simple cases of pairs of antennae. Only an outline of the rather bulky calculations has been given here, details being reserved for separate papers on some new antenna formulae. Although the paper is mainly concerned with demonstrating the above mentioned method for generating integral formulae, the compilation of formulae for mutual radiation resistance of antennae, mostly not published before, should be of interest for those working in antenna theory.