= Dual q-Krawtchouk polynomials
{wiki=Dual_q-Krawtchouk_polynomials}
The dual q-Krawtchouk polynomials are a family of orthogonal polynomials associated with the discrete probability distributions arising from the q-analog of the Krawtchouk polynomials. These polynomials arise in various areas of mathematics and have applications in combinatorics, statistical mechanics, and quantum groups. The Krawtchouk polynomials themselves are defined in terms of binomial coefficients and arise in the study of discrete distributions, particularly with respect to the binomial distribution.
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