# Tricky integral

1. Jun 8, 2014

### johnqwertyful

1. The problem statement, all variables and given/known data
$\int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dk$

2. Relevant equations

3. 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.

2. Jun 9, 2014

### 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.