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Laplace inversion

  1. Apr 26, 2012 #1
    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.
  2. jcsd
  3. Apr 26, 2012 #2
    Is it so that f(t) vanishes for t<0?
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