In mathematics, the q-Laguerre polynomials, or generalized Stieltjes–Wigert polynomials P(α)n(x;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme introduced by Daniel S. Moak (1981).
Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
The q-Laguerre polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by Orthogonality is defined by the unimono nature of the polynomials' convergence at boundaries in integral form.