Definition.
Orthogonality.
Recurrence relation.
where
and
Normalized recurrence relation.
where
q-Difference equation.
where
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
where
Generating function. For 
we have
Remark. The q-Krawtchouk polynomials defined by (3.15.1) and the dual q-Krawtchouk polynomials given by (3.17.1) are related in the following way :
with
or
with
References. [28], [62], [67], [104], [193], [323], [327], [384], [385].
