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 affine q-Krawtchouk polynomials defined by (3.16.1) and the big q-Laguerre polynomials given by (3.11.1) are related in the following way :
The affine q-Krawtchouk polynomials are related to the quantum
q-Krawtchouk polynomials defined by (3.14.1)
by the transformation 
in the following way :
References. [67], [119], [133], [134], [144], [169], [193], [385].
