Basic hypergeometric functions and orthogonal Laurent polynomials

Abstract

Abstract. A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials

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

“…It is easily verified that expression (2.12) for h n agrees with relation (1.3). The OPUC (2.9) can be considered as |q| = 1 analogs of the OPUC introduced by Askey in [1] (see also [3] for more general OPUC of Askey's type).…”

An explicit example of polynomials orthogonal on the unit circle with a dense point spectrum generated by a geometric distribution

“…The OPUC (2.9) can be considered as q = 1 analogs of the OPUC introduced by Askey in [1] (see also [3] for more general OPUC of Askey's type).…”

Orthogonal polynomials on the unit circle: Verblunsky coefficients with some restrictions imposed on a pair of related real sequences

“…Orthogonal polynomials on the unit circle (OPUC) have been commonly known as Szegő polynomials in honor of Gábor Szegő who introduced them in the first half of the 20th century. Because of their applications in quadrature rules, signal processing, operator and spectral theory and many other topics, these polynomials have received a lot of attention in recent years (see, for example, [2,4,7,12,13,16,17,21]). For many years a first hand text for an introduction to these polynomials has been the classical book [20] of Szegő.…”