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

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2012-01-01

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Alvarez-Nodarse, Renato
Adiguzel, Rezan Sevinik
Taşeli, Hasan

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

q-polynomials, Orthogonal polynomials on q-linear lattices, q-Hahn class

URI

https://hdl.handle.net/11511/46157

Journal

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS

DOI

https://doi.org/10.3842/sigma.2012.042

Collections

Department of Mathematics, Article

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Citation Formats

R. Alvarez-Nodarse, R. S. Adiguzel, and H. Taşeli, “On the Orthogonality of q-Classical Polynomials of the Hahn Class,” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, pp. 0–0, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46157.