正交多项式族的偏和变形

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-30 DOI:arxiv-2409.00261

Erik Koelink, Pablo Román, Wadim Zudilin

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引用次数: 0

摘要

关于附在正交多项式$\{p_n(x)\}_{n\ge0}$族上的多项式$q_m(x)=q_m(x;t)=\sum_{n=0}^mt^mp_n(x)$，人们可能会提出几个问题。在本论文中，我们将关注这种偏和变形的自然性以及相关的优美结构。特别是，我们将研究在实数参数 $t$ 变化的情况下，$q_m(x;t)$ 的零点的位置和分布。

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A partial-sum deformation for a family of orthogonal polynomials

There are several questions one may ask about polynomials $q_m(x)=q_m(x;t)=\sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal polynomials $\{p_n(x)\}_{n\ge0}$. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of $q_m(x;t)$ in the case of varying real parameter $t$.

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arXiv - MATH - Classical Analysis and ODEs

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