Q-difference Polynomial - Definition

Definition

The q-difference polynomials satisfy the relation

\left(\frac {d}{dz}\right)_q p_n(z) =
\frac{p_n(qz)-p_n(z)} {qz-z} = p_{n-1}(z)

where the derivative symbol on the left is the q-derivative. In the limit of, this becomes the definition of the Appell polynomials:

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