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Al-Salam–Carlitz polynomials
In mathematics, Al-Salam–Carlitz polynomials U(x;q) and V(x;q) are two families of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detailed list of their properties.
Definition
The Al-Salam–Carlitz polynomials are given in terms of basic hypergeometric functions by : U_n^{(a)}(x;q) = (-a)^nq^{n(n-1)/2}{}_2\phi_1(q^{-n}, x^{-1};0;q,qx/a) : V_n^{(a)}(x;q) = (-a)^nq^{-n(n-1)/2}{}_2\phi_0(q^{-n}, x;-;q,q^n/a)
References
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