The Q-Krawtchouk polynomials are a set of orthogonal polynomials that generalize the Krawtchouk polynomials, which themselves are a class of discrete orthogonal polynomials. The Krawtchouk polynomials arise in combinatorial settings and are connected to binomial distributions, while the Q-Krawtchouk polynomials introduce a parameter \( q \) that allows for further generalization. ### Definition and Properties 1.
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