Legendre Fit to the Reflection Coefficient of a Radiating Rectangular Waveguide Aperture

We accurately calculate the reflection coefficient and normalized admittance of radiating open-ended rectangular waveguides and fit our results with a linear combination of Legendre polynomials. We verify the expression to an accuracy of 0.005 with other calculations and examine the impact of flanges and burrs on the accuracy to which the reflection coefficient can be approximated in practice.