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

Year 2020, Volume: 3 Issue: 2, 75 - 84, 01.06.2020

Sergey Zagorodnyuk

https://doi.org/10.33205/cma.690236

Cited By: 3

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.

Keywords

Sobolev orthogonal polynomials, hypergeometric polynomials, unit circle, differential equation, recurrence relation

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