I want a document or something that explains the following proposition:

The discrete orthogonal polynomials are the polynomial solutions of the given diference equation: $$ \sigma(x)\Delta\nabla P_n(x) +\tau(x) \Delta P_n(x) + \lambda_nP_n (x) = 0, $$ where $\Delta P_n(x) = P_n(x + 1) -P_n(x)$ and $\nabla P_n(x) = P_n(x)-P_n(x-1)$ indicates backward fnite-diference operator and forward fnite diference operator, respectively. $\sigma (x)$ and $\tau (x)$ denote first and second degree functions. $\lambda_n$ indicate a suitable constant.

  • $\begingroup$ What is the proposition here? This looks rather as a definition. $\endgroup$ Commented Dec 3, 2023 at 17:36


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