Definition.
Orthogonality. If a is real and |a| < 1, then we have the following orthogonality relation
where
with
If a > 1, then we have another orthogonality relation given by :
where 
is as before,
and
Recurrence relation.
Normalized recurrence relation.
where
q-Difference equations.
where
If we define
then the q-difference equation can also be written in the form
where
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
Rodrigues-type formula.
Generating functions.
References. [58], [72], [73], [162].
