On characterizations of classical polynomials
The author presents a unified study of the classical discrete polynomials and \(q\)-polynomials of the \(q\)-Hahn tableau by using the difference calculus on linear-type lattices. He obtains several characterization theorems for the classical discrete and \(q\)-polynomials of the \(q\)-Hahn tableau. The classical continuous case can be obtained from the \(q\)-case by taking the limit \(q\leftarrow 1^{-}\). He also discusses some problems related to the characterization by \textit{F. Marcellán} et al. [Acta Appl. Math. 34, 283--303 (1994; Zbl 0793.33009)].
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