Inverse Laplace transformation of a complex function

Question

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?

See this solution and set $a=0$. – Ron Gordon Apr 22 '13 at 14:12 — Ron Gordon, Apr 22 '13 at 14:12

score 0 · Accepted Answer · answered Apr 22 '13 at 05:35

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

Inverse Laplace transformation of a complex function

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