Fourier transform question:

My professor has been using this equation for the fourier transform:$$F[f(\xi)]=\int\limits_{-\infty}^{\infty}f(x)e^{-i \xi x}dx$$

But I have a book that claims this is the fourier transform:
$$F[f(\xi)]=\frac{1}{\sqrt{2 \pi}}\int\limits_{-\infty}^{\infty}f(x)e^{-i \xi x}dx$$

So........ what's with the 1/sqrt(2 pi)?

For context, this is a PDE class.

Question

Fourier transform question:

My professor has been using this equation for the fourier transform:$$F[f(\xi)]=\int\limits_{-\infty}^{\infty}f(x)e^{-i \xi x}dx$$

But I have a book that claims this is the fourier transform:
$$F[f(\xi)]=\frac{1}{\sqrt{2 \pi}}\int\limits_{-\infty}^{\infty}f(x)e^{-i \xi x}dx$$

So........ what's with the 1/sqrt(2 pi)?

For context, this is a PDE class.

anonymous · Answer

I see a confusion about the fourier transform for angular and ordinary frequency http://en.wikipedia.org/wiki/Fourier_transform#Functional_relationships

ash2326 · Answer

@abstracted both are correct, some books use $2\pi$ with the fourier transform and some use it with inverse fourier transform.
Important thing is to use $2\pi$ only with one of them