:
Definitions. The continuous q-Laguerre polynomials can be
obtained from the continuous q-Jacobi polynomials defined by
(3.10.1) by taking the limit :
Orthogonality. For 
we have
where
with
Recurrence relations.
Normalized recurrence relations.
where
q-Difference equations.
where
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
Rodrigues-type formula.
Generating functions.
Remark. If we let 
tend to infinity in
(3.10.14) and renormalize we obtain
These two q-analogues of the Laguerre polynomials are connected by the following quadratic transformation :
Reference. [64].
