I need some help with this also:
Prove that :
FourierTransform[e^(-ax^2)]=(sqrt[Pi/a]) e^(-ω^2/4a)
Put
Differentiate:
Now take FTs of both sides and apply the derivative rules to the forward
and backwards transform:
so we have satisfies the ODE:
and all one now has to do is show that the suggested form for satisfies
this equation (or you could just solve the equation - it's of variables separable type).
(there is at least one other way of doing it, but that requires Cauchy's integral theorem from complex analysis)
RonL