We need some more differential and difference operators to formulate the Rodrigues-type formulas. These operators can also be used to formulate the second order differential or difference equations but this is mostly avoided. As usual we will use the notation
Further we define
and
Note that this implies that
Further we have for 
In a similar way we have for 
and hence for 
Also note that
For the Rodrigues-type formula in case of discrete orthogonal polynomials we often need to define an operator like
where 
depends on 
and 
,
for the following reason. For instance, the Rodrigues-type formula
(1.2.10) for the Racah polynomials can be obtained from
(1.2.9) by iteration. First we find from (1.2.9)
where 
. If we iterate this formula the
involved equals 
, 
respectively.
In a similar way we obtain from (3.2.10) for the q-Racah polynomials
where 
depends on 
and 
.
Iterating this formula we finally obtain the Rodrigues-type formula
(3.2.11) for the q-Racah polynomials. In this process the
involved equals 
, where
.
Finally we define
Here we have
