Inverse Fourier Transform of |k|^2$\lambda$

[johnqwertyful]

Homework Statement

\int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dk

Homework Equations

The Attempt at a Solution

As you can guess, this is the inverse Fourier transform of |k|^{2\lambda}. I've tried splitting it from -infinity to 0 and 0 to infinity. I've tried noting that |k| is even, cos is even, sin is odd and getting:

2\int_0^{\infty} |k|^{2\lambda}\cos(kx)dk
But this integral doesn't even converge.

 

[hilbert2]

I don't think the original integral converges either, no matter what the value of $\lambda$ is. Try using different values of $\lambda$ and $x$ and integrating numerically with a large interval of integration.