Doubling (Dual) Hahn Polynomials: Classification and Applications
We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeu...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147422 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Doubling (Dual) Hahn Polynomials: Classification and Applications / R. Oste, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 32 назв. — англ. |
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irk-123456789-1474222019-02-15T01:23:19Z Doubling (Dual) Hahn Polynomials: Classification and Applications Oste, R. Van der Jeugt, J. We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor. 44 (2011), 265203, 15 pages, arXiv:1101.5310]. Our classification shows there exist three dual Hahn doubles and four Hahn doubles. The same technique is then applied to Racah polynomials, yielding also four doubles. Each dual Hahn (Hahn, Racah) double gives rise to an explicit new set of symmetric orthogonal polynomials related to the Christoffel and Geronimus transformations. For each case, we also have an interesting class of two-diagonal matrices with closed form expressions for the eigenvalues. This extends the class of Sylvester-Kac matrices by remarkable new test matrices. We examine also the algebraic relations underlying the dual Hahn doubles, and discuss their usefulness for the construction of new finite oscillator models. 2016 Article Doubling (Dual) Hahn Polynomials: Classification and Applications / R. Oste, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 33C80; 81R05; 81Q65 DOI:10.3842/SIGMA.2016.003 http://dspace.nbuv.gov.ua/handle/123456789/147422 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor. 44 (2011), 265203, 15 pages, arXiv:1101.5310]. Our classification shows there exist three dual Hahn doubles and four Hahn doubles. The same technique is then applied to Racah polynomials, yielding also four doubles. Each dual Hahn (Hahn, Racah) double gives rise to an explicit new set of symmetric orthogonal polynomials related to the Christoffel and Geronimus transformations. For each case, we also have an interesting class of two-diagonal matrices with closed form expressions for the eigenvalues. This extends the class of Sylvester-Kac matrices by remarkable new test matrices. We examine also the algebraic relations underlying the dual Hahn doubles, and discuss their usefulness for the construction of new finite oscillator models. |
| format |
Article |
| author |
Oste, R. Van der Jeugt, J. |
| spellingShingle |
Oste, R. Van der Jeugt, J. Doubling (Dual) Hahn Polynomials: Classification and Applications Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Oste, R. Van der Jeugt, J. |
| author_sort |
Oste, R. |
| title |
Doubling (Dual) Hahn Polynomials: Classification and Applications |
| title_short |
Doubling (Dual) Hahn Polynomials: Classification and Applications |
| title_full |
Doubling (Dual) Hahn Polynomials: Classification and Applications |
| title_fullStr |
Doubling (Dual) Hahn Polynomials: Classification and Applications |
| title_full_unstemmed |
Doubling (Dual) Hahn Polynomials: Classification and Applications |
| title_sort |
doubling (dual) hahn polynomials: classification and applications |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147422 |
| citation_txt |
Doubling (Dual) Hahn Polynomials: Classification and Applications / R. Oste, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 32 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-11T02:02:42Z |
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2025-07-11T02:02:42Z |
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