A Property of Orthogonal Polynomial Families with Polynomial Duals

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Abstract
We show that for those discrete orthogonal polynomial families, ${ {p_i (mu (x))} }$, that have polynomial duals, the “finite convolution-type integral” operator, $sum olimits_{y = 0}^M {w(y)sum_{i = 0}^L {p_i (mu (x))} } p_i {{(mu (y))} / {h_i }}$, commutes with a second order difference operator.