Big q-Laguerre polynomials explained

In mathematics, the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition

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

P _{n(x;a,b;q) = (1)/((b ^{-1} q ^{-n} ;q) _{n})} {} _{2\phi} ^{- n} ^{1 \left(q} ,aqx ^{-1} ;aq;q, (x)/(b) \right)

Relation to other polynomials

Big q-Laguerre polynomials→Laguerre polynomials