Szegö polynomials: Some relations to \(L\)-orthogonal and orthogonal polynomials (Q1874143)

The authors consider the Szegö polynomials \(S_n(z)\) with real reflection coefficients and obtain some relations to certain self-inverse orthogonal \(L\)-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on a real line. The polynomials obtained by rotating the coefficients in the recursive relations satisfied by the self-inverse orthogonal \(L\)-polynomials have also been considered.