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 and the Pochhammer symbol by

Orthogonality

Recurrence and difference relations

Rodrigues formula

Generating function

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
，which is exactly Hahn polynomials.