  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.

Classical Analysis and ODEs