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.
The polynomials are given in terms of basic hypergeometric functions by
| qtm | |
| K | |
| n |
(q-x;p,N;q)={}2\phi
| -n | |
| 1\left[\begin{matrix} q |
,q-x\\ q-N\end{matrix} ;q;pqn+1\right] n=0,1,2,...,N.