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smcro5
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Homework Statement
Find the inverse Laplace Transform of [itex]\frac{1}{s}\frac{\sqrt{s}-1}{\sqrt{s}+1}[/itex]
Homework Equations
The complex inversion formula (well known)
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?