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The problem of a coaxially excited hollow probe in a rectangular waveguide has been analysed by an approach in which the electric field off the end of the probe is the unknown that may be obtained by the solution of an integral equation. The electric field is represented as the static gap field multiplied by a Chebyshev series. The unknown coefficients may be found from a matrix equation in which the square matrix has dominant diagonal terms. It is shown that this permits accurate results to be obtained by retaining only a few terms of the series. Expressions are derived for the exterior and interior current distributions, and for the admittance presented to the coaxial line from which the probe is driven. Comparison of theoretical and experimental results shows the theory to be very accurate.