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In this chapter are given necessary and sufficient conditions for theregularity of solutions of the functional equation appearing in the theory ofclassical orthogonal polynomials. In addition, we also present the functionalRodrigues formula and a closed formula for the recurrence coefficients. Wefinally used these results to solve some interesting research problemsconcerning characterization theorems.

On classical orthogonal polynomials on lattices and some characterization theorems