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Q-Meixner–Pollaczek polynomials
In mathematics, the q-Meixner–Pollaczek polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
Definition
The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by ：
: P_{n}(x;a\mid q) = a^{-n} e^{in\phi} \frac{(a^2;q)_n}{(q;q)_n}{}_3\phi_2(q^{-n}, ae^{i(\theta+2\phi)}, ae^{-i\theta}; a^2, 0 \mid q; q),\quad x=\cos(\theta+\phi).
References
References
- Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analoques, p 460, Springer
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