On a family of hypergeometric Sobolev orthogonal polynomials on the unit circle

Abstract

In this paper we study the following family of hypergeometric polynomials: $y_n(x)=\frac{(-1{)}^{\rho }}{n!}{x}^n{}_2{F}_0(-n,\rho ;-;-\frac{1}{x})$, depending on a parameter $\rho \in \mathbb{N}$. Differential equations of orders $\rho +1$ and $2$ for these polynomials are given. A recurrence relation for $y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure.

arXiv comment11 pages