The Laguerre polynomials can be obtained from the Meixner-Pollaczek polynomials defined by (1.7.1)
by the substitution ,
and letting :
The Laguerre polynomials can be obtained from the Jacobi polynomials defined by (1.8.1) by
letting and then :
If we take and in the definition
(1.9.1) of the Meixner polynomials and let we obtain
the Laguerre polynomials :
The Hermite polynomials defined by (1.13.1) can be obtained from the
Laguerre polynomials given by (1.11.1) by taking the limit
in the following way :