The little q-Laguerre (or Wall) polynomials defined by
(3.20.1) can be obtained from the big q-Laguerre
polynomials by taking in (3.11.1) and then
letting :
The little q-Laguerre (or Wall) polynomials defined by (3.20.1)
are little q-Jacobi polynomials with b = 0. So if we set b = 0 in the
definition (3.12.1) of the little q-Jacobi polynomials we
obtain the little q-Laguerre (or Wall) polynomials :
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) :