Continuous q-Laguerre polynomials

In mathematics, the continuous q-Laguerre 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^{(\alpha )}(x|q)=\frac{(q^{\alpha +1};q{)}_n}{(q;q{)}_n}$${}_3{\varphi }_2(q^{-n},q^{\alpha /2+1/4}{e}^{i\theta },q^{\alpha /2+1/4}{e}^{-i\theta };q^{\alpha +1},0|q,q)$

References

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