# Laplace inversion

1. Apr 26, 2012

### bruno67

Maybe I am just being stupid, but I don't understand why in the Laplace inversion formula

$$(\mathcal{L}^{-1} F)(t) = \frac{1}{2\pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} e^{st} F(s) ds$$
the contour of integration must be chosen so that $\sigma$ is greater than the real part of all singularities of $F(s)$. I would be very grateful if someone could explain this.

2. Apr 26, 2012

### bruno67

Is it so that f(t) vanishes for t<0?