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

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Constructive Mathematical Analysis
Volume:3 Issue:2
On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle

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

Pages : 75-84

View : 9 | Download : 7

Publication Date : 2020-06-01

Article Type : Research Paper

Abstract :In this paper we study the following family of hypergeometric polynomials: $y_ninsert ignore into journalissuearticles values(x); = \frac{ insert ignore into journalissuearticles values(-1);^\rho }{ n! } x^n {}_2 F_0insert ignore into journalissuearticles values(-n,\rho;-;-\frac{1}{x});$, 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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