Q-Charlier polynomials

In mathematics, the q-Charlier polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition
The polynomials are given in terms of the basic hypergeometric function by
 * $$\displaystyle C_n(q^{-x};a;q) = {}_2\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a).$$