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

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

and

2) [itex]\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) [/itex]

or alternative at 2)

2 bis) [itex] \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) [/itex]

Thanks for the help!

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# Green function in the plane

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