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