The equation arised in the paper:Exact and asympototic representations of the sound field in a stratified ocean.That is the equation(3.12) for solving the problem $$\Delta p+k^{2}p=-\delta(z-z_{0})\frac{\delta(r)}{2\pi r}$$ $$p|_{z=0}=0$$ $$p|_{z=-h}=0$$ where p is the acouotic press and $\delta$ is the Dirac mass at the point 0.They said:using the fact that $$(\frac{\partial^2}{\partial r^{2}}+\frac{1}{r}\frac{\partial}{\partial r}+ka_{n}^{2})H^{(1)}_{0}(ka_{n}r)=\frac{4i\delta(r)}{2\pi r}$$ where $H_{0}^{(1)}(ka_{n}r)$is the first kind Hankle Function of order zero.
Probelm:I don't know this fact because I can't derive from my knowledge.Please help me prove this equation.