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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Sprache: | English |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147422 |
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| Zitieren: | 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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Oste, R. Van der Jeugt, J. 2019-02-14T18:18:20Z 2019-02-14T18:18:20Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147422 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. The authors wish to thank the referees for their insightful remarks and suggestions which helped to enhance the clarity of the matter covered here. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Doubling (Dual) Hahn Polynomials: Classification and Applications Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Doubling (Dual) Hahn Polynomials: Classification and Applications |
| spellingShingle |
Doubling (Dual) Hahn Polynomials: Classification and Applications Oste, R. Van der Jeugt, J. |
| 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 |
| author |
Oste, R. Van der Jeugt, J. |
| author_facet |
Oste, R. Van der Jeugt, J. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
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| first_indexed |
2025-12-07T18:27:52Z |
| last_indexed |
2025-12-07T18:27:52Z |
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1850875128273960960 |