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arXiv.org e-Print Archive
Preprint . 2011
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https://dx.doi.org/10.48550/ar...
Article . 2011
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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: 1107.2423

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

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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