Difference equation of hypergeometric type

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The difference equation of hypergeometric type is of the form $$\sigma(n)\Delta \nabla y(n) + \tau(n) \Delta y(n) + \lambda y(n) =0,$$ where $\Delta$ is the forward difference operator and $\nabla$ is the backward difference operator, $\sigma$ and $\tau$ are polynomials of degree $\leq 2$, and $\lambda$ is a constant.

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