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It is stated and proved a characterization theorem for Laguerre-Hahnorthogonal polynomials on non-uniform lattices. This theorem proves theequivalence between the Riccati equation for the formal Stieltjes function,linear first-order difference relations for the orthogonal polynomials as wellas for the associated polynomials of the first kind, and linear first-orderdifference relations for the functions of the second kind.

Characterization theorem for Laguerre-Hahn orthogonal polynomials on non-uniform lattices