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Topic: Inverse / Laplace Transform Halved
Replies: 3   Last Post: Jun 14, 2009 7:07 PM

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Raul Martinez

Posts: 11
Registered: 5/14/07
Re: Inverse / Laplace Transform Halved
Posted: Jun 14, 2009 5:37 AM
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Mathematica 7.01 with MacOS 10.5.7 produces the following:

In[78]:= InverseLaplaceTransform[LaplaceTransform[BesselI[1, t], t, s], s, t]
Out[78]= Sqrt[=CF=80] InverseLaplaceTransform[=E2=89=A5 {
{-(s/Sqrt[=CF=80]), s < 1},
{((s (-1 + s/Sqrt[-1 + s^2]))/Sqrt[=CF=80]), s > 1},
{0,
TagBox["True",
"PiecewiseDefault",
AutoDelete->False,
DeletionWarning->True] }
}/s, s, t]

In[91]:= LaplaceTransform[InverseLaplaceTransform[s*Exp[(-a)*Sqrt[s]], s, t], t, s]
Out[91]= E^(-a Sqrt[s]) s

The second is the exact function in the argument. The first does not
process the three conditions of the LT of BesselI[1,t].

HTH,

Raul Martinez


On Jun 13, 2009, at 3:01 AM, Sid wrote:

> Dear MathGroup,
>
> I am currently using Version 6 and have found that
>
> InverseLaplaceTransform[LaplaceTransform[BesselI[1,t],t,s],s,t]
>
> yields, after tidying up, 1/2 BesselI[1,t].
>
>
> Also,
>
> LaplaceTransform[InverseLaplaceTransform[s*Exp[(-a)*Sqrt[s]], s, t],
> t,s]
>
> gives ((1/2)*s)/E^(a*Sqrt[s]) .
>
>
> Do members have the same problem with Version 7 ?
>
> Is it I who am missing something here ?
>
>
> Thanks for your help.
>
> Cheers
>
> Sid
>




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