Q-Hahn polynomials

In mathematics, the q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions by

Relation to other polynomials

q-Hahn polynomials→ Quantum q-Krawtchouk polynomials：
q-Hahn polynomials→ Hahn polynomials
make the substitution, into definition of q-Hahn polynomials, and find the limit q→1, we obtain