Little q-Jacobi.
Little q-Jacobi.
The little q-Jacobi polynomials defined by (3.12.1) can be obtained
from the big q-Jacobi polynomials by the substitution 
in the definition
(3.5.1) and then by the limit 
:
Little q-Jacobi.
If we set 
in the definition (3.6.1) of the q-Hahn
polynomials and take the limit 
we find the little q-Jacobi polynomials :
where 
is defined by (3.12.1).
Little q-Laguerre / Wall.
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 :
q-Laguerre.
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) :
Alternative q-Charlier.
If we set 
in the definition
(3.12.1) of the little q-Jacobi polynomials and then take
the limit 
we obtain the alternative q-Charlier polynomials given
by (3.22.1) :
