CAOP

q-Hahn Polynomials

Definition

The q-Hahn polynomials are defined as

\[ \begin{align} Q_n(q^{-x};a,b,N|q) &= \sum_{k=0}^\infty \frac{(q^{-n};q)_k (abq^{n+1};q)_k (q^{-x};q)_k}{(aq;q)_k (q^{-N};q)_k (q;q)_k} q^k\\ &= {}_{3}\phi_{2}\!\left(\left. {q^{-n}, abq^{n+1}, q^{-x} \atop aq, q^{-N}} \; \right| q ; q \right) \end{align} \]

q-Difference Equation

q-Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

\(q\)

Parameters

\(a\) \(0 < a < q^{-1}\)

\(b\) \(0 < b < q^{-1}\)

\(N\) \(N > 0\)

factor (use Maple-style input)

   q-hypergeometric term in \(n\) and q-hypergeometric term in \(q^{-x}\) required