- Askey Wilson
- q-Racah
- Continuous Dual q-Hahn
- Continuous q-Hahn
- Big q-Jacobi
- q-Hahn
- Dual q-Hahn
- Al Salam Chihara
- q-Meixner Pollaczek
- Continuous q-Jacobi
- Big q-Laguerre
- Little q-Jacobi
- q-Meixner
- Quantum q-Krawtchouk
- q-Krawtchouk
- Affine q-Krawtchouk
- Dual q-Krawtchouk
- Continuous Big q-Hermite
- Continuous q-Laguerre
- Little q-Laguerre / Wall
- q-Laguerre
- Alternative q-Charlier
- q-Charlier
- Al-Salam-Carlitz I
- Al-Salam-Carlitz II
- Continuous q-Hermite
- Stieltjes-Wigert
- Discrete q-Hermite I
- Discrete q-Hermite II
q-Hahn Polynomials
Definition
The q-Hahn polynomials are defined as
\[
\begin{align}
Q_n(q^{-x};a,b,N|q) &= \sum_{k=0}^\infty \frac{(q^{-n};q)_k (abq^{n+1};q)_k (q^{-x};q)_k}{(aq;q)_k (q^{-N};q)_k (q;q)_k} q^k\\
&= {}_{3}\phi_{2}\!\left(\left. {q^{-n}, abq^{n+1}, q^{-x} \atop aq, q^{-N}} \; \right| q ; q \right)
\end{align}
\]
