cylindrical polar co ordinates is

\begin{equation}

\int ^{r= ∞}_ {r=0} \int^ {z=∞} _{ z= - ∞} {δ(r) δ(z-z_s)} dz dr.

\end{equation}

where $r_s$ is $0$.

( green function) $G_{3D}= \frac{- 1}{4πσ r} = \frac{∂G}{∂r} + \frac{1}{r} ≈ 0$ on boundary $\Gamma_\infty$

where $r$ is $|X-X_0|$. $\sigma$ is constant with respect to one of the variables $r$ or $z$ but solution depend upon $r$ only.

No current flux on a surface with normal $n$: $ σ \frac{∂V}{∂n} =0$ [ Neumann boundary condition ]

now my question is how do I tackle the problem by using the boundary integral method with the help above equations.