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

[摘要] 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.

[关键词] q-polynomials;orthogonal polynomials on q-linear lattices;q-Hahn class