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This article is cited in 2 scientific papers (total in 2 papers)
On the orthogonality of $q$-classical polynomials of the Hahn class
Renato Álvarez-Nodarsea, Rezan Sevinik Adigüzelb, Hasan Taşelib a IMUS & Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, E-41080 Sevilla, Spain
b Department of Mathematics, Middle East Technical University (METU), 06531, Ankara, Turkey
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.
Keywords:
$q$-polynomials, orthogonal polynomials on $q$-linear lattices, $q$-Hahn class.
Received: July 29, 2011; in final form July 2, 2012; Published online July 11, 2012
Citation:
Renato Álvarez-Nodarse, Rezan Sevinik Adigüzel, Hasan Taşeli, “On the orthogonality of $q$-classical polynomials of the Hahn class”, SIGMA, 8 (2012), 042, 30 pp.
Linking options:
https://www.mathnet.ru/eng/sigma719 https://www.mathnet.ru/eng/sigma/v8/p42
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