Al-Salam–Chihara polynomials

In mathematics, the Al-Salam–Chihara polynomials Q_n(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al-Salam and Chihara (1976). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14.8) give a detailed list of the properties of Al-Salam–Chihara polynomials.

The Al-Salam–Chihara polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by

where x = cos(θ).

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