In mathematics, the continuous q-Jacobi polynomials P(α,β)n(x|q), introduced by Askey & Wilson (1985), are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.
Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by