Green's function of Laplace equation in axissymmetric bounded region

Question

Given a Laplace equation in an axissymmetric region, i.e., $\nabla^2 \varphi(r,z) = \frac{1}{r}\frac{\partial}{\partial r}\left(r \frac{\partial \varphi}{\partial r}\right) + \frac{\partial^2\varphi}{\partial z^2} = 0$, is is possible to find the close form of the Green's function $G(r,z;r',z')$ such that $\nabla^2 G(r,z;r',z') = \frac{1}{r}\frac{\partial}{\partial r} \left[ r \frac{\partial G(r,z;r',z')}{\partial r} \right] + \frac{\partial^2 G(r,z;r',z')}{\partial z^2} = -\delta(r-r',z-z')$ on the bounded region $\Omega = [r_1, r_2]\times[z_1, z_2]$ with the Dirichlet boundary condition $G(\mathbf{r}\in\partial\Omega; \mathbf{r}') = 0$? Here, $0 < r_1 < r' <r_2$ and $z_1 < z' < z_2$.