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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Author: Zhedanov, Alexei
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211079
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution. Alexei Zhedanov. SIGMA 16 (2020), 140, 9 pages

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 the -hypergeometric function of type ₂₁. The orthogonality measure is the wrapped geometric distribution. Some ''classical'' properties...