# Big q-Laguerre polynomials

In mathematics, the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

## Definition

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

$P_n(x;a,b;q)=\frac{1}{(b^{-1}*q^{-n};q,n)}*_2\Phi_1(q^{-n},aqx^{-1};aq|q;\frac{x}{b})$

## Relation to other polynomials

Big q-Laguerre polynomials→Laguerre polynomials