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If a physical network is approximated by a polynomial, the output wave may be expressed in terms of the derivatives of the input wave. This fact may be used to advantage in the solution of steady-state problems in FM, when the sideband method is impractical and the quasi-steady-state method invalid. If the range of approximation of the network function coincides with the nonnegligible part of the spectrum of the input wave, and if an orthogonal polynomial is chosen as the approximating function, then a practical method of solving steady-state FM problems can be established. In this paper, such a method is established, the various problems related to its validity are investigated, and examples of the method are demonstrated.