\(q\)-classical polynomials and the \(q\)-Askey and Nikiforov-Uvarov tableaus (Q5949512)

The authors continue the study of \(q\)-classical orthogonal polynomials started in [\textit{J. C. Medem, R. Álvarez-Nodarse} and \textit{F. Marcellán}, J. Comput. Appl. Math. 135, 157-196 (2001; Zbl 0991.33007)]. By using a characterization based on Hahn's \(q\)-derivative operator a partly classification is obtained for the classical \(q\)-orthogonal polynomials belonging to the \(q\)-Askey scheme of basic hypergeometric orthogonal polynomials. The authors concentrate on the discrete part of this scheme. The results are also compared with those of \textit{A. F. Nikiforov} and \textit{V. B. Uvarov} [Int. Trans. Spec. Funct. 1, 223-249 (1993; Zbl 1023.33002)].