Let μ be a finite positive measure defined on the Borelian σ−algebra of C, μ is absolutely continuous with respect to the Lebesgue measure dθ on [−π, +π]. Let us consider {L n (z)} n∈AE , the system of monic orthogonal polynomial with respect to μ. We introduce a new class of polynomials {P n } , that we call polar polynomials associated to {L n (z)} n∈AE. For a fixed complex number α, P n (z) is solution of the following differential equation (n + 1) L n (z) = P n (z) + (z − α) P n (z). we study algebraic and asymptotic properties of the polar polynomials {P n } n∈AE .

In this paper we derive useful results regarding the asymptotic properties of new set of monic polynomials primitives of orthogonal polynomials on the unit circle, called second order polar polynomials.

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