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The electromagnetic problem by the finite bicone, which is formed with the perfectly conducting semi-infinite cone and the finite cone with truncated vertex, is studied. Bicone is excited axial-symmetrically by the ring magnetic source.The diffracted field is represented through the series of the transversal magnetic (TM) modes; the lower mode among them is called the transversal electromagnetic wave (TEM). On the basis of this representation and using the mode matching technique, we derive the series equations to determine the unknown complex modes magnitudes. In view of the electric field singularities at the conical edges, these equations are represented in the form of the limiting transition from the finite sums to the series. We derive the rule of this transition, as well as the procedure for reducing them to the infinite system of linear algebraic equations (ISLAE) of the first kind. We study asymptotic properties of the matrix elements and find that the main part of their static limit and their behavior for large indexes form the matrix operator of the convolution type; the corresponding inverted operator in the analytical form is obtained. Both these operators, which we call the regularization operators, are used for the transition from the ISLAE of the first kind to the ISLAE of the second kind. The ISLAE thus obtained allow for the solution of any geometrical parameters and frequency with the given accuracy. The asymptotic properties of their solutions are analyzed, and the numerical examinations of the far field patterns are provided.

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