On the Orthogonality of q-Classical Polynomials of the Hahn Class

dc.contributor.authorÁlvarez-Nodarse, R.
dc.contributor.authorAdıgüzel, R.S.
dc.contributor.authorTaşeli, H.
dc.date.accessioned2019-02-18T12:56:54Z
dc.date.available2019-02-18T12:56:54Z
dc.date.issued2012
dc.description.abstractThe 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.sponsorshipWe 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.citationOn 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.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 33D45; 42C05
dc.identifier.otherDOI: http://dx.doi.org/10.3842/SIGMA.2012.042
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/148454
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleOn the Orthogonality of q-Classical Polynomials of the Hahn Classuk_UA
dc.typeArticleuk_UA

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