To obtain the dual q-Hahn polynomials from the q-Racah polynomials we have to
take and in (3.2.1) :
with
We may also take and in (3.2.1) to obtain the dual q-Hahn polynomials from the q-Racah polynomials :
with
And if we take , and in the definition (3.2.1) of the q-Racah polynomials we find the dual q-Hahn polynomials given by (3.7.1) in the following way :
with
The affine q-Krawtchouk polynomials defined by (3.16.1)
can be obtained from the dual q-Hahn polynomials by the substitution
and in (3.7.1) :
Note that in this case.
The dual q-Krawtchouk polynomials defined by (3.17.1) can
be obtained from the dual q-Hahn polynomials by setting
in (3.7.1) and then letting
: