%0 Journal Article
%T On the Orthogonality of q-Classical Polynomials of the Hahn Class
%A Renato ¨¢lvarez-Nodarse
%A Rezan Sevinik Ad£¿g¨¹zel
%A Hasan Ta£¿eli
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X 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.
%K q-polynomials
%K orthogonal polynomials on q-linear lattices
%K q-Hahn class
%U http://dx.doi.org/10.3842/SIGMA.2012.042