Question: special whittaker functions

January 25 2013 by
false
Maple

1

Hi

In trying to solve:

 a := diff(u(t), t\$2)+(p^2-I+t^2)*u(t) = 0;
I get the following solutions,
sol1 := u(t) = _C1*WhittakerM(-1/4-(1/4*I)*p^2, 1/4, I*t^2)/sqrt(t)+_C2*WhittakerW(-1/4-(1/4*I)*p^2, 1/4, I*t^2)/sqrt(t)

It should be possible to expand these into parabolic cylinder functions and but im not sure how, i would appreciate any help.
thanks