Fourier transformation

[Infernum]

Find the Fourier transformation of the function

[tex]f(x)=e^{-\sqrt{2}x^2}[/tex]

[adamsmith]

Given [tex]f(x)=e^{-\sqrt{2}x^2}[/tex]
the Fourier transformation [tex]f(t) =\int f(x)e^{-2\pi ixt}dx[/tex] from -infinity to +infinity
f(t)=∫e^(-√2x²)e^(-2πixt)) dx from -infinity to +infinity
f(t)=∫e^(-√2x²-2πixt) dx from -infinity to +infinity
f(t)=2∫e^(-√2x²-2πixt) dx from 0 to +infinity
f(t)=1/tπi

More information on Fourier Transform Equation at http://goo.gl/6lTeZc

[leesajohnson]

f(t)=∫f(x)e−2πixtdx