On the Orthogonality of q-Classical Polynomials of the Hahn Class
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Orthogonality of q-Classical Polynomials of the Hahn Class
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| Creator |
Álvarez-Nodarse, R.
Adıgüzel, R.S. Taşeli, H. |
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| Description |
The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation on a q-linear lattice by means of a qualitative analysis of the q-Pearson equation. To be more specific, a geometrical approach has been used by taking into account every possible rational form of the polynomial coefficients in the q-Pearson equation, together with various relative positions of their zeros, to describe a desired q-weight function supported on a suitable set of points. Therefore, our method differs from the standard ones which are based on the Favard theorem, the three-term recurrence relation and the difference equation of hypergeometric type. Our approach enables us to extend the orthogonality relations for some well-known q-polynomials of the Hahn class to a larger set of their parameters.
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| Date |
2019-02-18T12:56:54Z
2019-02-18T12:56:54Z 2012 |
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| Type |
Article
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| Identifier |
On the Orthogonality of q-Classical Polynomials of the Hahn Class / R. Álvarez-Nodarse, R.S. Adıgüzel, H. Taşeli // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33D45; 42C05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.042 http://dspace.nbuv.gov.ua/handle/123456789/148454 |
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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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