Meixner-Pollaczek.
Meixner-Pollaczek.
The Meixner-Pollaczek polynomials given by (1.7.1) can be obtained from the continuous dual Hahn polynomials
by the substitutions 
, 
, 
and 
in the definition
(1.3.1) and the limit 
:
Meixner-Pollaczek.
By taking 
, 
, 
and 
in the definition (1.4.1) of the continuous Hahn polynomials and taking the limit 
we obtain the Meixner-Pollaczek polynomials defined by (1.7.1) :
Laguerre.
The Laguerre polynomials can be obtained from the Meixner-Pollaczek polynomials defined by (1.7.1)
by the substitution 
,
and letting 
:
Hermite.
If we substitute 
in the definition (1.7.1) of the Meixner-Pollaczek polynomials and
then let 
we obtain the Hermite polynomials :
