Definition.
where
Orthogonality.
where
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 function. For 
we have
Remark. The dual q-Krawtchouk polynomials defined by (3.17.1) and the q-Krawtchouk polynomials given by (3.15.1) are related in the following way :
with
or
with
References. [119], [259], [279], [282].
