The Expansion of Wronskian Hermite Polynomials in the Hermite Basis

We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this, we deduce an upper bound for the modulus of the roots in the case of partitions of length 2. We also derive a general upper bound for the modulus of the real and purely imagi...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2021
Hauptverfasser: Grosu, Codruţ, Grosu, Corina
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2021
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211185
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The Expansion of Wronskian Hermite Polynomials in the Hermite Basis. Codruţ Grosu and Corina Grosu. SIGMA 17 (2021), 003, 14 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Grosu, Codruţ
Grosu, Corina
author_facet Grosu, Codruţ
Grosu, Corina
citation_txt The Expansion of Wronskian Hermite Polynomials in the Hermite Basis. Codruţ Grosu and Corina Grosu. SIGMA 17 (2021), 003, 14 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this, we deduce an upper bound for the modulus of the roots in the case of partitions of length 2. We also derive a general upper bound for the modulus of the real and purely imaginary roots. These bounds are very useful in the study of the irreducibility of Wronskian Hermite polynomials. Additionally, we generalize some of our results to a larger class of polynomials.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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last_indexed 2026-04-17T19:28:04Z
publishDate 2021
publisher Інститут математики НАН України
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spelling Grosu, Codruţ
Grosu, Corina
2025-12-25T13:25:19Z
2021
The Expansion of Wronskian Hermite Polynomials in the Hermite Basis. Codruţ Grosu and Corina Grosu. SIGMA 17 (2021), 003, 14 pages
1815-0659
2020 Mathematics Subject Classification: 26C10; 30C15; 34L40
arXiv:2006.15534
https://nasplib.isofts.kiev.ua/handle/123456789/211185
https://doi.org/10.3842/SIGMA.2021.003
We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this, we deduce an upper bound for the modulus of the roots in the case of partitions of length 2. We also derive a general upper bound for the modulus of the real and purely imaginary roots. These bounds are very useful in the study of the irreducibility of Wronskian Hermite polynomials. Additionally, we generalize some of our results to a larger class of polynomials.
The authors are indebted to the referees for the careful reading and for suggesting extending the results to q ≥ 3.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
Article
published earlier
spellingShingle The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
Grosu, Codruţ
Grosu, Corina
title The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
title_full The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
title_fullStr The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
title_full_unstemmed The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
title_short The Expansion of Wronskian Hermite Polynomials in the Hermite Basis
title_sort expansion of wronskian hermite polynomials in the hermite basis
url https://nasplib.isofts.kiev.ua/handle/123456789/211185
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