q-Meixner.
q-Meixner.
If we take the limit 
in the definition (3.5.1) of the
big q-Jacobi polynomials we simply obtain the q-Meixner polynomials defined by
(3.13.1) :
q-Meixner.
The q-Meixner polynomials defined by (3.13.1 can be obtained from the q-Hahn polynomials
by setting 
and 
in the definition (3.6.1) of the
q-Hahn polynomials and letting 
:
q-Laguerre.
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
:
q-Charlier.
The q-Meixner polynomials and the q-Charlier polynomials defined by (3.13.1)
and (3.23.1) respectively are simply related by the limit 
in the definition (3.13.1) of the q-Meixner polynomials. In fact we have
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 
:
