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Inverse Laplace Transform and Branch Points

  1. Oct 13, 2011 #1
    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?
  2. jcsd
  3. Oct 14, 2011 #2
    Isn't s=1 a singular point? That is, what is the multi-valued square root of 1?
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