# Inverse Laplace transform of a function having algebraic singularity

Submitted by Structure on Sat, 12/22/2007 - 22:59.

Laplace inverse transform of

This function has two singular points, zero and none of them isolated.

We use the differential equation satisfied by F:

Let

Then

So

Or

Or

Or

or

Now

and

But is equivalent at to and then their Laplace transform are equivalent at s=0 But

From

we have

.

Finally we have