Q:

Inverse Laplace transformation of a complex function

Consider the complex function $\displaystyle f(s)=\frac{1}{\frac lc\sqrt{(s(s+r_0)}}$ where $r_0, l, c$ are positive real number and s is a complex variable. How I can obtain the inverse Laplace transformation of this function?  

A:

I have found the following formula about my question. 
$$L^{-1}\{\frac{1}{\sqrt{s+a}\sqrt{s+b}}\}=e^{-\frac{(a+b)t}{2}}I_0(\frac{a-b}{2}t)$$
where $I_0(x)$ is modified Bessel function.
But I have another question. I put it in this site. It would be grateful if someone can help me.
Thanks

