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arXiv · 1107.2423

The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach

R. Alvarez-Nodarse·R. Sevinik-Adiguzel·H. Taseli
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Abstract

The idea of this review article is to discuss in a unified way the orthogonality of all positive definite polynomial solutions of the $q$-hypergeometric difference equation on the $q$-linear lattice by means of a qualitative analysis of the $q$-Pearson equation. 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. A short version of this paper appeared in SIGMA 8 (2012), 042, 30 pages http://dx.doi.org/10.3842/SIGMA.2012.042.

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R. Alvarez-Nodarse, R. Sevinik-Adiguzel, H. Taseli. 2012-07-11. The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach. https://doi.org/10.3842/sigma.2012.042

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