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dc.contributor.author |
Álvarez-Nodarse, R. |
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dc.contributor.author |
Adıgüzel, R.S. |
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dc.contributor.author |
Taşeli, H. |
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dc.date.accessioned |
2019-02-18T12:56:54Z |
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dc.date.available |
2019-02-18T12:56:54Z |
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dc.date.issued |
2012 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 33D45; 42C05 |
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dc.identifier.other |
DOI: http://dx.doi.org/10.3842/SIGMA.2012.042 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/148454 |
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dc.description.abstract |
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. |
uk_UA |
dc.description.sponsorship |
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. |
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dc.language.iso |
en |
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dc.publisher |
Інститут математики НАН України |
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dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
On the Orthogonality of q-Classical Polynomials of the Hahn Class |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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