This paper describes a method to obtain an analytical expression for the nonlinear dependence of the ferroelectric polarization on the external electric field. To find analytical dependence, used a special K_ml-function of second order. Listed structure built of series and groups  of series representing K_ml-function at any point in the complex plane. Analyzed domain of  convergence of series , received as a boundary condition. To show the application of the method, as  an example used a ferroelectric polymer polyvinylidene fluoride (PVDF–TrFE ). The proposed method can be used for any other ferroelectric or nonlinear systems ordered in the neighborhood of phase transitions under various external influences.