## Inverse Laplace transform of a function having algebraic singularity

Posted December 22nd, 2007 by Structure

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