A Property of Orthogonal Polynomial Families with Polynomial Duals

Authors:
  • MPMarci Perlstadt
    Marci Perlstadt
  • RPRonald Keith Perline
    Ronald Keith Perline
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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, $\sum\nolimits_{y = 0}^M {w(y)\sum_{i = 0}^L {p_i (\mu (x))} } p_i {{(\mu (y))} / {h_i }}$, commutes with a second order difference operator.

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