Definition.
Orthogonality. If a and b are real or complex conjugates and
, then we have the following orthogonality relation
where
with
If a > 1 and |ab| < 1, then we have another orthogonality relation given by :
where 
is as before,
and
Recurrence relation.
Normalized recurrence relation.
where
q-Difference equation.
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. [13], [19], [20], [55], [58], [73], [125], [132], [164], [236], [239], [261], [262].
