Big q-Laguerre polynomials

In mathematics, the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Template:Harvs have given a detailed list of their properties.

Definition

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

$P_n(x;a,b;q)=\frac{1}{(b^{-1}{q}^{-n};q{)}_n}{}_2{\varphi }_1(q^{-n},aq{x}^{-1};aq;q,\frac{x}{b})$

Relation to other polynomials

Big q-Laguerre polynomials→Laguerre polynomials

References

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