CAOP

Alternative q-Charlier Polynomials

Definition

The Alternative q-Charlier polynomials are defined as

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

q-Difference Equation

q-Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

\(q\)

Parameters

\(a\) \(a > 0\)

factor (use Maple-style input)

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