Consider the complex function f(s)=(1)/(l/c sqrt((s(s+r_0))) where r_0,l,c are positive real number and s is a complex variable.

Jensen Mclean 2022-09-06 Answered
Consider the complex function $f\left(s\right)=\frac{1}{\frac{l}{c}\sqrt{\left(s\left(s+{r}_{0}\right)}}$ 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?
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Jordan Owen
I have found the following formula about my question.
${L}^{-1}\left\{\frac{1}{\sqrt{s+a}\sqrt{s+b}}\right\}={e}^{-\frac{\left(a+b\right)t}{2}}{I}_{0}\left(\frac{a-b}{2}t\right)$
where ${I}_{0}\left(x\right)$ is modified Bessel function.