Hi,

I want to find the inverse laplace transform of $\displaystyle f(s)=\frac{1}{\sqrt{s^{2}+a^{2}}}$. I know that the inverse is $\displaystyle F(t)=J_0(at)$ from the tables, but I need to know how it is found. Does it have anything to do with branch points in complex domain?

I do appreciate it if someone can solve it for me and tell me the inversion process.