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[tex]\int\limits_{ - \infty }^\infty {\int\limits_{ - \infty }^\infty {e^{ixy} dxdy = 2\pi}}[/tex]

(x,y, real)

It came out analyzing the relation between DiracDelta and the Fourier Transform formula. (it's the reason why insert the constant 1/sqrt(2pi) in the fourier transform formula to be consistent with the diracdelta definition).

I know that it's value is 2pi. But I'd like to see how to actually calculate it. (Possibly in some elegant way...)

There must be some tricky "magic" based on symmetry consideration to reduce the double integral to the length of a unit circle. But I can't find it.

Thanks