q-Laguerre polynomials

Template:See also In mathematics, the q-Laguerre polynomials, or generalized Stieltjes–Wigert polynomials PTemplate:Su(x;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme introduced by Template:Harvs. Template:Harvs give a detailed list of their properties.

Definition

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

$L_n^{(\alpha )}(x;q)=\frac{(q^{\alpha +1};q{)}_n}{(q;q{)}_n}{}_1{\varphi }_1(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x).$

Orthogonality

Orthogonality is defined by the unimono nature of the polynomials' convergence at boundaries in integral form.

References

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