Systems of Transcendental Equations with Polynomial Representation of Solutions in Free- Phase Problems

The integral equations of the Hammerstein type are considered. New method is proposed for the analytical-numerical solution of these equations. It is based on the property of the logarithmic derivative when calculating the argument of a complex function in its polynomial representation. The derived systems of transcendental and integral-transcendental equations are used for solving the equations under consideration. Equations for possible branching points of solutions in the polynomial form are obtained.