Does a Fourier transform exist for this (smooth) f.?

[rachmaninoff]

e^{-x^2}\cos \left( e^{x^2} \right)

Mathematica doesn't have an algorithm for it, does a closed form exist for the Fourier transform? It's continuously differentiable on all intervals in R, and it converges to zero at the infinities (the derivative blows up there).

 

[cogito²]

e^{-x^2}\cos \left( e^{x^2} \right)

Mathematica doesn't have an algorithm for it, does a closed form exist for the Fourier transform? It's continuously differentiable on all intervals in R, and it converges to zero at the infinities (the derivative blows up there).

Well after looking at it for a few minutes on paper, I'd say I certainly doubt you'll get anything nice out of that. Also if Mathematica can't do it, I doubt I'll find an answer as well.