I am interested to learn about the Green function for the D'Alembert operator in arbitrary dimensions. While searching through the web I came across the following document:
There the fundamental solution for the general Green function is given in eq. (14). Special cases for 3, 2 and 1 dimensions are given further below. Now, I was trying to start with eq. (14) and reduce it to the 3 dimensional result eq. (15) by setting $d=3$ and taking the appropriate limit - but I do not get the same result. In fact, restricting to the imaginary part I actually get zero in the limit $\epsilon\rightarrow 0^+$. It would be great if someone could demonstrate how to do this. Thanks for any suggestion!