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Laplace transform of erf

  1. Jan 8, 2006 #1
    how do i find the laplace transform of the following error function without using tables?
    f(t)=erf(t^(1/2))
    i've been trying really long but i seem to be stuck in a loop of erf
     
  2. jcsd
  3. Jan 8, 2006 #2

    saltydog

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    Hey Jarain. Suppose you mean other than Mathematica right?

    Just perform the integrations directly then:

    [tex]\mathcal{L}\left\{\text{Erf}[\sqrt{t}]\right\}=
    \int_0^{\infty}e^{-st}\left[\frac{2}{\sqrt{\pi}}\int_0^{\sqrt{t}} e^{-u^2}du\right]dt[/tex]

    Now, can you switch the order of integrations to effect the solution?
     
    Last edited: Jan 8, 2006
  4. Jan 8, 2006 #3

    Tide

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    Try integrating by parts.
     
  5. Jan 8, 2006 #4

    saltydog

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    Nice! Thanks.:smile:

    Well, then do it both ways Jarain. :rolleyes:

    Edit: Oh yea. Tide's way is better.:smile:
     
  6. Apr 20, 2011 #5
    Hi! I actually just performed this transform recently.
    Let dv/dt = [tex]\int e^{-st}[/tex]
    Let u = [tex]\int_0^{\sqrt{t}} e^{-x^2} dx[/tex]
     
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