I have been studying Fourier transforms lately. Specifically, I have been studying the form of the formula that uses the square root of 2π in the definition. Now here is the problem: In some sources, I see the forward and inverse transforms defined as such: F(k) = [1/(√2π)] ∫∞-∞ f(x)eikx dx f(x) = [1/(√2π)] ∫∞-∞ f(k)eikx dk In other cases, I've seen: F(k) = [1/(√2π)] ∫∞-∞ f(x)e-ikx dx f(x) = [1/(√2π)] ∫∞-∞ f(k)eikx dk Notice that in the first version of the forward transform (the one that solves for F(k)), the exponential in the integrand has a positive sign in the exponent ikx, while in the 2nd version it has a negative ikx. Which version is correct? Are they both correct and it is a matter of convention? Are neither correct? Also, is there some way to do a multiple dimensional Fourier transform using volume integrals? If so, what is the formula for that (preferably including (√2π))?