Dual Hahn.
If we take
and let
in (1.2.1),
then we obtain the dual Hahn polynomials from the Racah polynomials. So we have

And if we take
and let
in (1.2.1),
then we also obtain the dual Hahn polynomials :

Finally, if we take
and
in the definition
(1.2.1) of the Racah polynomials and take the limit
we find the dual Hahn polynomials given by
(1.6.1) in the following way :

Meixner.
To obtain the Meixner polynomials from the dual Hahn polynomials we have to take
and
in the definition (1.6.1) of
the dual Hahn polynomials and let
:

Krawtchouk.
In the same way we find the Krawtchouk polynomials from the dual Hahn polynomials
by setting
,
in (1.6.1) and let
:
