4.7 Dual q-Hahn

q-Racah Dual q-Hahn.

  
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

Dual q-Hahn Affine q-Krawtchouk.

  
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.

Dual q-Hahn Dual q-Krawtchouk.

  
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 :




Last modified on July 7, 1998