The antenna synthesis problem according to the prescribed power radiation pattern with the equality norm condition is considered. It is solved by the approach based on the concept of generating polynomials. The variational formulation, supplied by the Lagrange method of multipliers, is applied. The Lagrange--Euler equation for obtained functional is a nonlinear integral equation of the Hammerstein type. The polynomial approach is described for a generalized equation of this type, which holds for different types of antennas. The modified Newton method is used for numerical solving of the respective systems of integro-transcendental equation. The approach is applied to the concrete problems related to the linear antenna, equidistant antenna array, and the circular aperture antenna. The numerical results are obtained and analyzed.

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