On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle

Abstract

In this paper, we study the following family of hypergeometric polynomials:yn(x) = (−1)ρn!xn2F0(−n, ρ; −; − 1x), depending on a parameter ρ ∈ N. Differential equations of orders ρ+1 and 2 forthese polynomials are given. A recurrence relation for yn is derived as well. Polynomials yn are Sobolev orthogonalpolynomials on the unit circle with an explicit matrix measure.