# Laplace inverse transform formula and Cauchy's integral formula

The question is about Laplace Transform and the inverse transform formula.

Can the inverse transform formula be proved using Cauchy's integral formula?

-
Context please? –  Jonas Teuwen May 5 '11 at 17:48
Cauchy's integral formula only applies to holomorphic functions, whereas the Laplace transform works on much more general functions, so I don't see how this would work without some nontrivial extra steps. –  Qiaochu Yuan May 5 '11 at 18:31
The thing is, Laplace transform is an analytic function (at least in some domain), even if the previous function wasn't. I can apply Cauchy's integral formula to actually compute the inverse transform integral, but only for specific cases (and not for a general case). –  Maxim May 6 '11 at 0:03