q-Laguerre polynomials

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

${\displaystyle \displaystyle L_{n}^{(\alpha )}(x;q)={\frac {(q^{\alpha +1};q)_{n}}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x).}$

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

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