A Two-Parameter Family of Orthogonal Polynomials with Respect to a Jacobi-Type Weight on the Unit Circle

AbstractA two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight ωα,β(θ)=|(1−z)α(1+z)β|2, α,β>− 1 2 , z=eiθ. Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [−1,1] is presented