On the Orthogonality of q-Classical Polynomials of the Hahn Class
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 appro...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148454 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862545366761603072 |
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| author | Álvarez-Nodarse, R. Adıgüzel, R.S. Taşeli, H. |
| author_facet | Álvarez-Nodarse, R. Adıgüzel, R.S. Taşeli, H. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-25T07:14:46Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148454 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T07:14:46Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Álvarez-Nodarse, R. Adıgüzel, R.S. Taşeli, H. 2019-02-18T12:56:54Z 2019-02-18T12:56:54Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148454 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. We thank the referees for their careful reading of the manuscript and the suggestions that helped us to improve the paper. This work was partially supported by MTM2009-12740-C03-02 (Ministerio de Econom´ıa y Competitividad), FQM-262, FQM-4643, FQM-7276 (Junta de Andaluc´ıa), Feder Funds (European Union), and METU OYP program (RSA). The second author (RSA) thanks the Departamento de An´alisis Matem´atico and IMUS for their kind hospitality during her stay in Sevilla. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Orthogonality of q-Classical Polynomials of the Hahn Class Article published earlier |
| spellingShingle | On the Orthogonality of q-Classical Polynomials of the Hahn Class Álvarez-Nodarse, R. Adıgüzel, R.S. Taşeli, H. |
| title | On the Orthogonality of q-Classical Polynomials of the Hahn Class |
| title_full | On the Orthogonality of q-Classical Polynomials of the Hahn Class |
| title_fullStr | On the Orthogonality of q-Classical Polynomials of the Hahn Class |
| title_full_unstemmed | On the Orthogonality of q-Classical Polynomials of the Hahn Class |
| title_short | On the Orthogonality of q-Classical Polynomials of the Hahn Class |
| title_sort | on the orthogonality of q-classical polynomials of the hahn class |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148454 |
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