I have $\alpha,\alpha_{0}$ complex numbers.
Now I would like to calculate the following:
$$\lim\limits_{\epsilon\rightarrow +0}\int\limits_{0}^{+\infty}r^{1-\epsilon}dr\int\limits_{0}^{r}r_{1}^{\epsilon-1}J_{0}(\left|\alpha r-\alpha_{0}r_{1}\right|)dr_{1}$$
where $J_{0}$ is a Bessel function. Any suggestions? However, I suspect this limit to be infinite...