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 ${_2}\phi_1$. The orthogonality measure is the wrapped geometric distribution. Some "classical" properties of the above polynomials are presented.