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Q-Laguerre polynomials
In mathematics, the q-Laguerre polynomials, or generalized Stieltjes–Wigert polynomials P(x;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme introduced by . 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 :\displaystyle L_n^{(\alpha)}(x;q) = \frac{(q^{\alpha+1};q)_n}{(q;q)_n} {}_1\phi_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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