This paper treats the solution of the -vector Helmholtz equation for the case of a plane electromagnetic wave at ’nose-on' incidence, on a perfectly-conducting cone of finite size* The solution presented is exact and in the form of an infinite series of spherical harmonics. The expansion coefficients of the series are determined by a set of an infinite number of equations involving an infinite number of unknowns. A discussion and numerical investigation of the field singularities at the tip and edge of the cone are included* as well as graphs of the associated Legendre functions of non-integral degree, P1(cos θ), and their first derivatives

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