- #1
johnqwertyful
- 397
- 14
Homework Statement
[itex]\int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dk[/itex]
Homework Equations
The Attempt at a Solution
As you can guess, this is the inverse Fourier transform of [itex]|k|^{2\lambda}[/itex]. 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:
[itex]2\int_0^{\infty} |k|^{2\lambda}\cos(kx)dk [/itex]
But this integral doesn't even converge.