Inverse Laplace Transform and Branch Points

[smcro5]

Homework Statement

Find the inverse Laplace Transform of $\frac{1}{s}\frac{\sqrt{s}-1}{\sqrt{s}+1}$

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 $\frac{1}{s}$ 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 $\sqrt{s}$ has a branch point at s=0. Therefore the function has a branch point at s=0. Performing a substitution s=$\frac{1}{t}$ into $\sqrt{s}$ 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?

 

[jackmell]

Isn't s=1 a singular point? That is, what is the multi-valued square root of 1?