If we substitute and in the definition
(3.12.1) of the little q-Jacobi polynomials and then let b tend to
infinity we find the q-Laguerre polynomials given by (3.21.1) :
The q-Laguerre polynomials defined by (3.21.1) can be obtained
from the q-Meixner polynomials given by (3.13.1) by setting
and in the definition
(3.13.1) of the q-Meixner polynomials and then taking the limit
:
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) :