Universidad de Sevilla. Departamento de Análisis Matemático2014-11-272014-11-2720121815-0659http://www.emis.de/journals/SIGMA/2012/042/sigma12-042.pdfhttp://hdl.handle.net/11441/16110The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric dif ference 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 coef ficients 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 dif fers from the standard ones which are based on the Favard theorem, the three-term recurrence relation and the dif ference 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.enghttp://creativecommons.org/licenses/by-nc-nd/4.0/q-polynomialsorthogonal polynomials on q-linear latticesq-Hahn classinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.3842/SIGMA.2012.042https://idus.us.es/xmlui/handle/11441/16110