Consider the differential equation satisfied by

(1) 
where is a Whittaker Function.

(2) 

(3) 
This is usually rewritten

(4) 
The solutions are Parabolic Cylinder Functions.
The equations

(5) 

(6) 
which arise by separating variables in Laplace's Equation in Parabolic Cylindrical Coordinates, are also
known as the Weber differential equations. As above, the solutions are known as Parabolic Cylinder Functions.
© 19969 Eric W. Weisstein
19990526