Coaxially fed hollow cylindrical monopole in a rectangular waveguide

A formally exact solution that can easily be put in a form suitable for accurate numerical calculation is presented for a hollow coaxially fed cylindrical monopole in a rectangular waveguide. The solution utilises a well known Fourier-transform technique in conjunction with a Chebyshev polynomial representation for the unknown function. The result is an almost diagonalised infinite matrix—a form eminently suitable for the purpose of numerical inversion.