A two-parameter family of orthogonal polynomials with respect to Jacobi-type weight on the unit circle
A family of orthogonal polynomials on the unit circle associated with a weight of Jacobi type was studied. Recursion formulas, explicit representations, some algebraic properties and norm properties are given. An explicit connection to the Jacobi polynomials was established using the Szegő theory for orthogonal polynomials on the unit circle. Identities holding for Jacbi polynomials were used to obtain identities for the polynomials on the unit circle. Asymptotic properties, orthogonal expansion, or norm estimates on arcs of the unit circle were not considered.
scientific article; zbMATH DE number 1417583