I am trying to solve the integral $$\int\frac1{p^2}\exp(i\vec{p}\cdot(\vec{r}+i\vec{R}))\,\mathrm d\vec{p}.$$I learned from [1] that$$\int\frac1{p^2}\exp(i\vec{p}\cdot\vec{r})\,\mathrm d\vec{p}=\frac{2\pi^2}{r}.$$May I ask if it's OK to replace $r$ by $|\vec{r}+i\vec{R}|$ to get the integral? If not, any suggestions on how to solve it?
Many thanks!
====================== Update 04/16/20 ==========================
One more question, is it possible to get the Fourier transformation of $$\frac{1}{|\vec{r}+i\vec{R}|}$$
Thanks!
Reference:
[1]. https://arxiv.org/pdf/1302.1830.pdf