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arXiv · 2002.06428

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

Sergey M. Zagorodnyuk
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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.

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Sergey M. Zagorodnyuk. 2020-02-15. On a family of hypergeometric Sobolev orthogonal polynomials on the unit circle. https://arxiv.org/abs/2002.06428

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