Solutions of the ``dispersion relation'' for an unbounded Maxwellian electron plasma, 2k2/kD2 = Z′(ω/kvth) for ω real are given. Solutions of the corresponding relation for a circular waveguide filled with a hot plasma with an infinite magnetostatic field are also presented. It is shown that these solutions are of importance in evaluating the fields in such waveguides since they determine the poles of the integrands which arise in the integral formulation of the problem. The integral solution for the field in the waveguide due to a general symmetric excitation at the wall of the waveguide is given.
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