CAOP

Dual q-Krawtchouk Polynomials

Definition

The Dual q-Krawtchouk polynomials are defined as

\[ \begin{align} K_n(\lambda(x);c,N|q) &= \sum_{k=0}^\infty \frac{(q^{-n};q)_k (q^{-x};q)_k (cq^{x-N};q)_k}{(q^{-N};q)_k (q;q)_k} q^k\\ &= {}_{3}\phi_{2}\!\left(\left. {q^{-n}, q^{-x}, cq^{x-N} \atop q^{-N}, 0} \; \right| q ; q \right) \end{align} \]

q-Difference Equation

q-Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

\(q\)

Parameters

\(c\) \(c < 0\)

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

factor (use Maple-style input)

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