In mathematics, the affine q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Carlitz and Hodges.
Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
The polynomials are given in terms of basic hypergeometric functions by [1] affine q-Krawtchouk polynomials → little q-Laguerre polynomials：