In mathematics, the little q-Laguerre polynomials pn(x;a|q) or Wall polynomials Wn(x; b,q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme closely related to a continued fraction studied by . (The term "Wall polynomial" is also used for an unrelated Wall polynomial in the theory of classical groups.) give a detailed list of their properties.
The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by
\displaystylepn(x;a|q)={}2\phi
| -n | |
| 1(q |
,0;aq;q,qx)=
| 1 | |
| (a-1q-n;q)n |
{}2\phi
| -n | |
| 0(q |
,x-1;;q,x/a)