An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution

Abstract

We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of q-hypergeometric function of type 2phi1. The orthogonality measure is the wrapped geometric distribution. Some classical properties of the above polynomials are presented.