See also: continuous q-Hahn polynomials, dual q-Hahn polynomials and continuous dual 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.
The polynomials are given in terms of basic hypergeometric functions by
| -x | |
| Q | |
| n(q |
;a,b,N;q)={}3\phi2\left[\begin{matrix}q-n,abqn+1,q-x\ aq,q-N\end{matrix};q,q\right].
q-Hahn polynomials→ Quantum q-Krawtchouk polynomials：
\limaQn(q-x
| qtm | |
| ;a;p,N|q)=K | |
| n |
(q-x;p,N;q)
q-Hahn polynomials→ Hahn polynomials
make the substitution
\alpha=q\alpha
\beta=q\beta
{}3F2(-n,\alpha+\beta+n+1,-x,\alpha+1,-N,1)