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Re: does anybody know how to find the inverse Laplace transform of this wierd thing?


"gino" <loseminds at hotmail.com>
> Want to find the inverse Laplace transform of the following term:
>
> H(s)=1/s^2*exp(s^2*a^2/2)*integrate(exp(-u^2/2), u from s*a to +infinity)
>
> How to do that?
>
> ------------------------------
>
> Making relaxation to the problem, if I have to find only certain sampled
> values of the inverse Laplace transform of H(s), let's denote it as h(t),
>
> I just need to find h(1), h(2), h(3), etc.
>
> Is there a short cut for it?
>
> Thanks a lot!
>
>
Gino,
I've given your H[s_]:= ...  function to Math5.2 running on WinXP
and I've obtained this result in few seconds with 
InverseLaplaceTransform[H[s],s,t] :

\!\(\@\(\[Pi]\/2\)\ \((a\ \((\(-1\) + \[ExponentialE]\^\(-\(t\^2\/\(2\ 
a\^2\)\
\)\))\)\ \@\(2\/\[Pi]\) + t\ Erf[t\/\(\@2\ a\)])\)\)

(paste it in your Mathematica front-end)
Assuming 'a' as a constant and t is the new variable.

Bye,
    ~Scout~



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