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

A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight w,,,(e) = 1(1 - z)"(l + Z ) ~ I ʹ , a , p > - i, z = e l s . Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [ - 1, 11 is presented