- #1
bruno67
- 32
- 0
Maybe I am just being stupid, but I don't understand why in the Laplace inversion formula
[tex](\mathcal{L}^{-1} F)(t) = \frac{1}{2\pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} e^{st} F(s) ds[/tex]
the contour of integration must be chosen so that [itex]\sigma[/itex] is greater than the real part of all singularities of [itex]F(s)[/itex]. I would be very grateful if someone could explain this.
[tex](\mathcal{L}^{-1} F)(t) = \frac{1}{2\pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} e^{st} F(s) ds[/tex]
the contour of integration must be chosen so that [itex]\sigma[/itex] is greater than the real part of all singularities of [itex]F(s)[/itex]. I would be very grateful if someone could explain this.