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

Details 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

2011-07-12

arxiv.org/abs/1107.2423v4

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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