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Main Authors: Koelink, Erik, Román, Pablo, Zudilin, Wadim
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2409.00261
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author Koelink, Erik
Román, Pablo
Zudilin, Wadim
author_facet Koelink, Erik
Román, Pablo
Zudilin, Wadim
contents 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 $t$.
format Preprint
id arxiv_https___arxiv_org_abs_2409_00261
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A partial-sum deformation for a family of orthogonal polynomials
Koelink, Erik
Román, Pablo
Zudilin, Wadim
Classical Analysis and ODEs
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 $t$.
title A partial-sum deformation for a family of orthogonal polynomials
topic Classical Analysis and ODEs
url https://arxiv.org/abs/2409.00261