If we set and in the definition
(3.11.1) of the big q-Laguerre polynomials and take the
limit we obtain the Al-Salam-Carlitz I polynomials given by
(3.24.1) :
If we set in the definition (3.17.1)
of the dual q-Krawtchouk polynomials and take the limit
we simply obtain the Al-Salam-Carlitz I polynomials
given by (3.24.1) :
Note that .
The discrete q-Hermite I polynomials defined by
(3.28.1) can easily be obtained from the
Al-Salam-Carlitz I polynomials given by (3.24.1) by the
substitution a = -1 :