Al-Salam–Carlitz polynomials

In mathematics, Al-Salam–Carlitz polynomials U(a)
n(x;q) and V(a)
n(x;q) are two families of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al-Salam and Carlitz (1965). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14.24, 14.25) give a detailed list of their properties.

The Al-Salam–Carlitz polynomials are given in terms of basic hypergeometric functions by

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