论文标题
在单位圆上的超几何sobolev正交多项式上
On a family of hypergeometric Sobolev orthogonal polynomials on the unit circle
论文作者
论文摘要
在本文中，我们研究了以下超几何多项式的家族：$ y_n（x）= \ frac {（--1）^ρ} {n！ } x^n {} _2 f_0（-n，ρ; - ; - \ frac {1} {x} $，具体取决于参数$ρ\ in \ mathbb {n} $。给出了这些多项式的订单的微分方程$ρ+1 $和$ 2 $。 $ y_n $的复发关系也被得出。多项式$ y_n $是单位圆的Sobolev正交多项式，具有明确的矩阵度量。
In this paper we study the following family of hypergeometric polynomials: $y_n(x) = \frac{ (-1)^ρ}{ n! } x^n {}_2 F_0(-n,ρ;-;-\frac{1}{x})$, depending on a parameter $ρ\in\mathbb{N}$. Differential equations of orders $ρ+1$ 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.
