4.27 Stieltjes-Wigert

q-Laguerre Stieltjes-Wigert.

  
If we set in the definition (3.21.1) of the q-Laguerre polynomials and take the limit we simply obtain the Stieltjes-Wigert polynomials given by (3.27.1) :

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

q-Charlier Stieltjes-Wigert.

  
If we set in the definition (3.23.1) of the q-Charlier polynomials and take the limit we obtain the Stieltjes-Wigert polynomials given by (3.27.1) in the following way :




Last modified on July 7, 1998