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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2011Embargo end date: 01 Jan 2011Publisher:arXiv

Authors: Alvarez-Nodarse, R.; Sevinik-Adiguzel, R.; Taseli, H.;

doi: 10.48550/arxiv.1107.2423

arXiv: http://arxiv.org/abs/1107.2423

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

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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.

A short version of this paper appeared in SIGMA 8 (2012), 042, 30 pages http://dx.doi.org/10.3842/SIGMA.2012.042

Keywords

Mathematics - Classical Analysis and ODEs, 33D45, 42C05, Classical Analysis and ODEs (math.CA), FOS: Mathematics

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On the Orthogonality of q-Classical Polynomials of the Hahn Class
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The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach

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

1 Research products, page 1 of 1

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