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MathGroup Archive 2006

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64149] Re: [mg64100] does anybody know how to find the inverse Laplace transform of this wierd thing?
  • From: <bsyehuda at gmail.com>
  • Date: Thu, 2 Feb 2006 02:17:07 -0500 (EST)
  • References: <200602010934.EAA23043@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

InverseLaplaceTransform[1/s^2*Exp[s^2*a^2/2]*Integrate[Exp[-
    u^2/2], {u, s a, ∞}], s, t]
results with
Sqrt[Pi/2]*(a*(-1 + E^(-(t^2/(2*a^2))))*Sqrt[2/Pi] +
   t*Erf[t/(Sqrt[2]*a)])
However,
I do not have time to check the validity of the result
yehuda

On 2/1/06, gino <loseminds at hotmail.com> wrote:
>
> 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!
>
>
>



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