Mellin Transform Method for Integral Evaluation

This monograph presents the Mellin transform as a technique for evaluating integrals and shows how it applies to problems in electromagnetics. After the basic ideas are in place, the method proves unusually strong, frequently producing closed-form results that are hard to reach by other routes or to find in standard integral tables. Its procedure is simple to follow, though it tends to involve lengthy algebra rather than clever insight. The generalized hypergeometric function and the Meijer G-function both arise naturally with this approach, and modern numerical software can now evaluate them automatically, which makes them far more practical than before. The opening chapters cover the transform and these two functions. The rest of the book works through three examples, whose results appear to be new in the antenna and electromagnetics literature. The first gives a closed form, written as a generalized hypergeometric function, for the power radiated by a constant-current circular-loop antenna. The second addresses the admittance of a two-dimensional slot antenna. In both cases the exact expressions improve on formulas found in standard antenna textbooks. The third derives a very simple expression for an integral that comes up in unpublished work on unbounded, biaxially anisotropic media. Several further examples are discussed briefly.