Quantum q-Krawtchouk polynomials

In mathematics, the quantum q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition
The polynomials are given in terms of basic hypergeometric functions by
 * $$K_n^{qtm}(q^{-x};p,N;q)={}_2\phi_1\left[\begin{matrix}

q^{-n},q^{-x}\\ q^{-N}\end{matrix}
 * q;pq^{n+1}\right]\qquad n=0,1,2,...,N.$$