In mathematics, the q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
Stanton (1981) showed that the q-Krawtchouk polynomials are spherical functions for 3 different Chevalley groups over finite fields, and Koornwinder (1989) showed that they are related to representations of the quantum group SU(2).
Definition
The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol.
References
Q-Krawtchouk polynomials Wikipedia(Text) CC BY-SA