4.16 Affine q-Krawtchouk

q-Hahn Affine q-Krawtchouk.

  
The affine q-Krawtchouk polynomials defined by (3.16.1) can be obtained from the q-Hahn polynomials by the substitution and in (3.6.1) :

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.

Affine q-Krawtchouk Little q-Laguerre / Wall.

    
If we set in the definition (3.16.1) of the affine q-Krawtchouk polynomials and take the limit we simply obtain the little q-Laguerre (or Wall) polynomials defined by (3.20.1) :




Last modified on July 7, 1998