q-Krawtchouk.
q-Krawtchouk.
The q-Krawtchouk polynomials defined by (3.15.1) can be obtained from
the q-Racah polynomials by setting 
, 
and
in the definition (3.2.1) of the q-Racah polynomials :
Note that 
in this case.
q-Krawtchouk.
If we set 
in the definition (3.6.1) of the q-Hahn polynomials
and then let 
we obtain the q-Krawtchouk polynomials defined by
(3.15.1) :
Alternative q-Charlier.
If we set 
in the definition (3.15.1) of the
q-Krawtchouk polynomials and then take the limit 
we
obtain the alternative q-Charlier polynomials defined by
(3.22.1) :
q-Charlier.
The q-Charlier polynomials given by (3.23.1) can be obtained
from the q-Krawtchouk polynomials defined by (3.15.1) by
setting 
in the definition (3.15.1) of the
q-Krawtchouk polynomials and then taking the limit 
:
