2007/11/29 by Alexei Zhedanov, Zhedanov, Alexei
Mathematics · #33C47 #33E05 #33E20 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #math.CA #msc:33C47 #msc:33E05 #msc:33E20
paper · pdf · doi:10.48550/arxiv.0711.4696
28 pages
openalex publication_date 2007/11/29 · arxiv created 2007/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a new type of elliptic hypergeometric function. We show that obtained polynomials are orthogonal on the unit circle with respect to a dense point meausure, i.e. the spectrum consists from infinite number points of increase which are dense on the unit circle. We construct also corresponding explicit systems of polynomials orthogonal on the interval of the real axis with respect to a dense point measure. They can be considered as an elliptic generalization of the Askey-Wilson polynomials of a special type.