# Why does this Fourier transform not match the formula?

So I'm trying to get that result in Mathematica. From the fourier formula above, we can see that {a, b} = {1,-1}.

However, the code below returns a different result.

FourierTransform[Cos[2 \[Pi] A t], t, w, FourierParameters -> {1, -1}]
(*\[Pi] DiracDelta[2 A \[Pi] - w] + \[Pi] DiracDelta[2 A \[Pi] + w]*)

Is there anything wrong here?

• The result is true, its linked pseudo-proof is not: that improper integral diverges. The Fourier transforms of distributions are not defined as improper integrals (see "Tempered distributions" section in Wiki). I am sure those Fourier transforms are implemented as table values in Mathematica. May 22 at 5:49