
SIGMA, 2012, Volume 8, 042, 30 pages
(Mi sigma719)




This article is cited in 2 scientific papers (total in 2 papers)
On the orthogonality of $q$classical polynomials of the Hahn class
Renato ÁlvarezNodarse^{a}, Rezan Sevinik Adigüzel^{b}, Hasan Taşeli^{b} ^{a} IMUS & Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, E41080 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 threeterm recurrence relation and the difference equation of hypergeometric type. Our approach enables us to extend the orthogonality relations for some wellknown $q$polynomials of the Hahn class
to a larger set of their parameters.
Keywords:
$q$polynomials, orthogonal polynomials on $q$linear lattices, $q$Hahn class.
DOI:
https://doi.org/10.3842/SIGMA.2012.042
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ArXiv:
1107.2423
MSC: 33D45; 42C05 Received: July 29, 2011; in final form July 2, 2012; Published online July 11, 2012
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Renato ÁlvarezNodarse, Rezan Sevinik Adigüzel, Hasan Taşeli, “On the orthogonality of $q$classical polynomials of the Hahn class”, SIGMA, 8 (2012), 042, 30 pp.
Citation in format AMSBIB
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\paper On the orthogonality of $q$classical polynomials of the Hahn class
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\vol 8
\papernumber 042
\totalpages 30
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This publication is cited in the following articles:

VerdeStar L., “Recurrence Coefficients and Difference Equations of Classical Discrete Orthogonal and QOrthogonal Polynomial Sequences”, Linear Alg. Appl., 440 (2014), 293–306

F. Soleyman, M. MasjedJamei, I. Area, “A finite class of qorthogonal polynomials corresponding to inverse gamma distribution”, Anal. Math. Phys., 7:4 (2017), 479–492

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