In mathematics, the q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme . give a detailed list of their properties.
showed that the q-Krawtchouk polynomials are spherical functions for 3 different Chevalley groups over finite fields, and showed that they are related to representations of the quantum group SU(2).
The polynomials are given in terms of basic hypergeometric functions by
| -x | |
| K | |
| n(q |
;p,N;q)={}3\phi
| -n | |
| 2\left[\begin{matrix} q |
,q-x,-pqn\\ q-N,0\end{matrix} ;q,q\right], n=0,1,2,...,N.