Definition.
Orthogonality.
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.
where
Generating functions. For 
we have
Remarks. The quantum q-Krawtchouk polynomials defined by (3.14.1) and the q-Meixner polynomials given by (3.13.1) are related in the following way :
The quantum q-Krawtchouk polynomials are related to the affine
q-Krawtchouk polynomials defined by (3.16.1)
by the transformation 
in the following way :
References. [193], [277], [279].
