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MathGroup Archive 2004

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Re: Laplace Transformation vs. erf

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52983] Re: Laplace Transformation vs. erf
  • From: "Robert M. Mazo" <mazo at uoregon.edu>
  • Date: Sat, 18 Dec 2004 04:00:20 -0500 (EST)
  • Organization: University of Oregon
  • References: <cpudss$g9b$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Fri, 17 Dec 2004 10:54:20 +0000 (UTC), db at ict.fhg.de (julia) wrote:

>Hi,
>
>I have a problem with the following transformation:
>
>LaplaceTransform[Erf[(L - 2*t*v)/(2*(Dz*t)^0.5)], t, s]
>
>It seems that it doesn't converge because of the t in the numerator.

It converges allright.  Sketch the function.  It is bounded.
Therefore its Laplace Transform converges.

>When i take the t out of the expression, everything works fine.
>I've played a little bit around with assumptions and other options, but
>i couldn't work it out. v,L and Dz are parameters, which are all positive.


>I'm using t up to ~100.
>
>Mathematica just returns the input, and gives not even a error message...
>
>Can anybody help me with this?
>
>julia

I believe that you have just found a function whose Laplace Transform
Mathematica doesn't know.  These are not particularly rare.  After
all, given the task of evaluating the definite integral of an
arbitrary function, as smooth and well behaved as you wish, so that
the integral exists, why should you expect the result to come out as a
nice analytical formula in terms of a finite number of known
functions?  The Laplace Transform is just such an integral.  Many
times you are lucky and can evaluate the result analytically.  Often
you are unlucky and cannot.

Of course you can find the Laplace Transform numerically for as many
values of s as you want.  Use NIntegrate.

Bob


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