Doubling (Dual) Hahn Polynomials: Classification and Applications
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Doubling (Dual) Hahn Polynomials: Classification and Applications
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| Creator |
Oste, R.
Van der Jeugt, J. |
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| 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.
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| Date |
2019-02-14T18:18:20Z
2019-02-14T18:18:20Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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