4.22 Alternative q-Charlier

Little q-Jacobi Alternative q-Charlier.

  
If we set in the definition (3.12.1) of the little q-Jacobi polynomials and then take the limit we obtain the alternative q-Charlier polynomials given by (3.22.1) :

q-Krawtchouk 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) :

Alternative q-Charlier Stieltjes-Wigert.

  
The Stieltjes-Wigert polynomials defined by (3.27.1) can be obtained from the alternative q-Charlier polynomials by setting in the definition (3.22.1) of the alternative q-Charlier polynomials and then taking the limit . In fact we have