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: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| 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| _version_ | 1862747117909442560 |
|---|---|
| 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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| first_indexed | 2026-04-17T19:28:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211185 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T19:28:04Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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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