Jacobi.
Jacobi.
The Jacobi polynomials given by (1.8.1) can be found from the Wilson
polynomials by substituting 
, 
,
and 
in the
definition (1.1.1) of the Wilson polynomials and taking the limit
. In fact we have
Jacobi.
The Jacobi polynomials defined by (1.8.1) follow from the continuous Hahn polynomials
by the substitution 
, 
,
, 
and 
in (1.4.1), division by 
and the limit 
:
Jacobi.
To find the Jacobi polynomials from the Hahn polynomials we take 
in (1.5.1) and let 
We have
Laguerre.
The Laguerre polynomials can be obtained from the Jacobi polynomials defined by (1.8.1) by
letting 
and then 
:
Hermite.
The Hermite polynomials given by (1.13.1) follow from the Jacobi polynomials
defined by (1.8.1) by taking 
and letting
in the following way :
Hermite.
The Hermite polynomials given by (1.13.1) follow from the
Gegenbauer (or ultraspherical) polynomials defined by (1.8.15)
by taking 
and letting 
in the
following way :
