Definition.
Orthogonality. For 
and b < 0 we have
Recurrence relation.
where
Normalized recurrence relation.
where
q-Difference equation.
where
and
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
Generating functions.
Remark. The big q-Laguerre polynomials defined by (3.11.1) and the affine q-Krawtchouk polynomials given by (3.16.1) are related in the following way :
References. [13], [27], [228].
