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) :
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
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 :