q-Meixner–Pollaczek polynomials

In mathematics, the q-Meixner–Pollaczek polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Template:Harvs give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by ：

$P_n(x;a\mid q)=a^{-n}{e}^{in\varphi }\frac{(a^2;q{)}_n}{(q;q{)}_n}{}_3{\varphi }_2(q^{-n},a{e}^{i(\theta +2\varphi )},a{e}^{-i\theta };a^2,0\mid q;q),x=\cos (\theta +\varphi ).$

References

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