In mathematics, the q-Hahn 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.
The polynomials are given in terms of basic hypergeometric functions by q-Hahn polynomials→ Quantum q-Krawtchouk polynomials：
lim
q-Hahn polynomials→ Hahn polynomials make the substitution
into definition of q-Hahn polynomials, and find the limit q→1, we obtain