CAOP

Little q-Laguerre / Wall Polynomials

Definition

The Little q-Laguerre / Wall polynomials are defined as

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

q-Differential Equation

q-Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

\(q\)

Parameters

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

factor (use Maple-style input)

   q-hypergeometric term in \(n\) and q-hyperexponential term in \(x\) required