- #1

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## Main Question or Discussion Point

I've never really thought about this before, but today it hit me: Why do we define the Fourier transform of a function to be

[tex]

\hat f(k) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty f(x) e^{ikx} dx

[/tex]

What do we lose if we just define it to be

[tex]

\hat f(k) = \int_{-\infty}^\infty f(x) e^{ikx} dx

[/tex]

[tex]

\hat f(k) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty f(x) e^{ikx} dx

[/tex]

What do we lose if we just define it to be

[tex]

\hat f(k) = \int_{-\infty}^\infty f(x) e^{ikx} dx

[/tex]