Evaluation of a class of integrals occurring in mode matching solutions for electrical and electromagnetic modelling

Summary. Many integrals that go to make up the matrix for mode matching solutions of electrical or electromagnetic problems may be evaluated in closed form.
Examples where this is possible include the electrical problems of finding the potential about a point electrode that is in a layered ground that includes either a spherical or cylindrical conductor. The results given here greatly reduce the amount of computation that is required for the calculations proposed by Lee.
The integrals that arise analogous to the electromagnetic scattering of a cylinder in a half space may also be evaluated. For the case of a spherical scatter it is only possible to evaluate the integrals for the case where the source is a large coaxial loop.