Recurrence Relations for Wronskian Hermite Polynomials
We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees smaller, which generalizes the well-known three-term recurrence relation for Hermite polynomials. The...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209524 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Recurrence Relations for Wronskian Hermite Polynomials / N. Bonneux, M. Stevens // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862538216205189120 |
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| author | Bonneux, N. Stevens, M. |
| author_facet | Bonneux, N. Stevens, M. |
| citation_txt | Recurrence Relations for Wronskian Hermite Polynomials / N. Bonneux, M. Stevens // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees smaller, which generalizes the well-known three-term recurrence relation for Hermite polynomials. The polynomials are defined using partitions of natural numbers, and the coefficients in the recurrence relation can be expressed in terms of the number of standard Young tableaux of these partitions. Using the recurrence relation, we provide another recurrence relation and show that the average of the considered polynomials with respect to the Plancherel measure is very simple. Furthermore, we show that some existing results in the literature are easy corollaries of the recurrence relation.
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| first_indexed | 2025-12-03T06:25:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209524 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T06:25:09Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bonneux, N. Stevens, M. 2025-11-24T10:40:00Z 2018 Recurrence Relations for Wronskian Hermite Polynomials / N. Bonneux, M. Stevens // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05A17; 12E10; 26C05; 33C45; 65Q30 arXiv: 1801.07980 https://nasplib.isofts.kiev.ua/handle/123456789/209524 https://doi.org/10.3842/SIGMA.2018.048 We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees smaller, which generalizes the well-known three-term recurrence relation for Hermite polynomials. The polynomials are defined using partitions of natural numbers, and the coefficients in the recurrence relation can be expressed in terms of the number of standard Young tableaux of these partitions. Using the recurrence relation, we provide another recurrence relation and show that the average of the considered polynomials with respect to the Plancherel measure is very simple. Furthermore, we show that some existing results in the literature are easy corollaries of the recurrence relation. We thank Arno Kuijlaars and Walter Van Assche for fruitful discussions and a careful reading of a preliminary version of this article. The authors are supported in part by the long-term structural funding-Methusalem grant of the Flemish Government, and by the EOS project 30889451 of the Flemish Science Foundation (FWO). Marco Stevens is also supported by the Belgian Interuniversity Attraction Pole P07/18, and by FWO research grant G.0864.16. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Recurrence Relations for Wronskian Hermite Polynomials Article published earlier |
| spellingShingle | Recurrence Relations for Wronskian Hermite Polynomials Bonneux, N. Stevens, M. |
| title | Recurrence Relations for Wronskian Hermite Polynomials |
| title_full | Recurrence Relations for Wronskian Hermite Polynomials |
| title_fullStr | Recurrence Relations for Wronskian Hermite Polynomials |
| title_full_unstemmed | Recurrence Relations for Wronskian Hermite Polynomials |
| title_short | Recurrence Relations for Wronskian Hermite Polynomials |
| title_sort | recurrence relations for wronskian hermite polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209524 |
| work_keys_str_mv | AT bonneuxn recurrencerelationsforwronskianhermitepolynomials AT stevensm recurrencerelationsforwronskianhermitepolynomials |