Al-Salam-Carlitz II.
Al-Salam-Carlitz II.
The Al-Salam-Carlitz II polynomials defined by (3.25.1)
can be obtained from the q-Meixner polynomials defined by (3.13.1)
by setting 
in the definition (3.13.1) of the
q-Meixner polynomials and then taking the limit 
:
Al-Salam-Carlitz II.
If we set 
in the definition (3.14.1)
of the quantum q-Krawtchouk polynomials and let 
we
obtain the Al-Salam-Carlitz II polynomials given by
(3.25.1). In fact we have
Discrete q-Hermite II.
The discrete q-Hermite II polynomials defined by
(3.29.1) follow from the Al-Salam-Carlitz II
polynomials given by (3.25.1) by the substitution a = -1
in the following way :
