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Al-Salam–Chihara polynomials
Family of basic hypergeometric orthogonal polynomials in the basic Askey scheme
Family of basic hypergeometric orthogonal polynomials in the basic Askey scheme
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 . give a detailed list of the properties of Al-Salam–Chihara polynomials.
Definition
The Al-Salam–Chihara polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by : Q_n(x;a,b;q) = \frac{(ab;q)_n}{a^n}{}_3\phi_2(q^{-n}, ae^{i\theta}, ae^{-i\theta}; ab,0; q,q) where x = cos(θ).
References
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