A representation in error functions for the current and field of a horizontal wire above ground excited by a delta function voltage generator is studied. This representation involves contributions from both proper and improper solutions of the modal equation and makes it possible to assess the relative importance of proper and improper solutions in the radiation mechanism. The new representation requires the analytic continuation of the field tranforms into the whole complex plane of the transverse wave number which is studied for the first time as far as the improper half plane is concerned. An asymptotic expression for the radiation field is obtained, and it is shown that the principal improper mode provides a good approximation to the far field.
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