(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the inverse Laplace Transform of [itex]\frac{1}{s}\frac{\sqrt{s}-1}{\sqrt{s}+1}[/itex]

2. Relevant equations

The complex inversion formula (well known)

3. The attempt at a solution

The first thing is finding singularities and branch points and so on. From the [itex]\frac{1}{s}[/itex] part of the function, it seems as though s=0 is a simple pole (a pole of order one). However, it is known that each [itex]\sqrt{s}[/itex] has a branch point at s=0. Therefore the function has a branch point at s=0. Performing a substitution s=[itex]\frac{1}{t}[/itex] into [itex]\sqrt{s}[/itex] shows that the point at infinity is a branch point as well. I am about to start using the complex inversion formula, but am not sure about whether I have taken into account all the possible branch points/singularities.

Any ideas guys?

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# Inverse Laplace Transform and Branch Points

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