How to get the Fourier tramsform of $ |x|^{-\alpha} $ ; $ |x| = \sqrt{x_{1}^{2}+ ...+ x_{n}^{2}}$ ($x $ is multivariable).
I really stuck here, I want to derive the Riesz potential using Fourier transform, I found in Wikipedia that $$ \mathcal{F}(|x|^{-\alpha}) = c_{n-\alpha,n}(2 \pi)^{\alpha-n} |\mathbf{\xi}|^{-(n - \alpha)}$$ where $ \mathcal{F}$ stands for Fourier transform, and $$ c_{n-\alpha,n} = \pi^\frac{n}{2} 2^{\alpha}\frac{\Gamma(\frac{\alpha}{2})}{\Gamma(\frac{n-\alpha}{2})} $$. Any one can help me derive this expression?