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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 Waleed Al-Salam and Leonard Carlitz. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw give a detailed list of their properties.