Hahn.
Hahn.
If we take 
and let 
in the definition (1.2.1)
of the Racah polynomials, we obtain the Hahn polynomials defined by (1.5.1). Hence
The Hahn polynomials can also be obtained from the Racah polynomials by
taking 
in the definition (1.2.1) and letting
:
Another way to do this is to take 
and 
in
the definition (1.2.1) of the Racah polynomials and then take the
limit 
. In that case we obtain the Hahn polynomials
given by (1.5.1) in the following way :
Jacobi.
To find the Jacobi polynomials from the Hahn polynomials we take 
in (1.5.1) and let 
We have
Meixner.
If we take 
, 
in the definition (1.5.1)
of the Hahn polynomials and let 
we find the Meixner
polynomials given by (1.9.1) :
Krawtchouk.
If we take 
and 
in the definition (1.5.1)
of the Hahn polynomials and let 
we obtain the
Krawtchouk polynomials defined by (1.10.1) :
