Inverse Laplace Transform (Proof?)

[John Creighto]

According go Wikipedia the inverse Laplace Transform is given by:

$$\mathcal{L}^{-1} \{F(s)\} = f(t) = \frac{1}{2\pi i}\lim_{T\to\infty}\int_{\gamma-iT}^{\gamma+iT}e^{st}F(s)\,ds,$$

How do you probe this? I'm surprised that it doesn't depend on the value of $$\gama$$

http://en.wikipedia.org/wiki/Inverse_Laplace_transform

 

[matematikawan]

I think the proof can be found in most standard Laplace transform textbook. I have seen one in Schaum's Outline Series in Laplace Transform.

What is interesting about the Inverse Laplace Transform is the Post's inversion formula available at Wikipedia link. This inversion formula doesn't involve singularities but we need to compute derivatives of higher order.

Do anyone know any efficient method to compute higher order derivative f^(k)(x) ?