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What is the inverse laplace transform of this?

  1. Jun 12, 2010 #1
    [tex]F(s) = \frac{1}{K^s}[/tex]

    where K is a positive real.
  2. jcsd
  3. Jun 13, 2010 #2

    Write this as exp[-s Log(k)]

    Then compare this to the Laplace integral:

    Integral of exp(-s t) f(t) dt

    So, it looks like if you take f(t) to be a function that has a very large peak around t = Log(K), you'll get the correct Laplace transform up to some normalization. Now think of making this line of reasoning more precise...
  4. Jun 13, 2010 #3
    So is it [tex]\delta(t-\log(K))[/tex]?
  5. Jun 13, 2010 #4
    That's right!
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