# Green function in the plane

1. Feb 7, 2013

### santale

Hi everybody.

Does someone know the solution of the following differential equation in two dimensions:

1) $\Big(\frac{\partial^2}{\partial\,r^2}+\frac{ \partial^2}{\partial\,z^2}\Big)G(r,z)=\delta(r-ro)\delta(z-zo)$

and

2) $\Big(\frac{\partial^2}{\partial\,r^2}+\frac{1}{r}\frac{\partial}{\partial r}+\frac{\partial^2}{\partial\,z^2}\Big)G(r,z)= \delta(r-ro)\delta(z-zo)$

or alternative at 2)

2 bis) $\Big(\frac{\partial^2}{\partial\,r^2}-\frac{3}{4\,r}+\frac{\partial^2}{\partial\,z^2} \Big)G(r,z)=\delta(r-ro)\delta(z-zo)$

Thanks for the help!