I need help to calculate Fourier transform in distribution sense of $\frac{e^{i|x|}}{|x|}$ in $D'(\mathbb{R}^3)$ we have $ \frac{e^{i|x|}}{|x|} \in L^1_{loc}(\mathbb{R}^3)$
edit, Let $E(x)=\frac{e^{i|x|}}{|x|}$, i have $\langle\hat E,\phi\rangle=\langle E,\hat \phi\rangle=\int_{R^3}\int_{R^3}\frac{e^{i|\xi|}}{|\xi|}e^{-i\xi.x}\phi(x)dx\,d\xi$
Thanks