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On the orthogonality of q-classical polynomials of the Hahn class


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Opened Access On the orthogonality of q-classical polynomials of the Hahn class

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Author: Taseli, Hasan
Álvarez Nodarse, Renato
Sevinik, Rezan
Date: 2012
Published in: Symmetry, Integrability and Geometry : Methods and Applications, 8, 1-30.
Document type: Article
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 dif ference 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 coef ficients 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 dif fers from the standard ones which are based on the Favard theorem, the three-term recurrence relation and the dif ference 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.
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DOI: 10.3842/SIGMA.2012.042

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