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Re: Inverse / Laplace Transform Halved

• To: mathgroup at smc.vnet.net
• Subject: [mg100789] Re: [mg100753] Inverse / Laplace Transform Halved
• From: Raul Martinez <raulmart at mac.com>
• Date: Sun, 14 Jun 2009 05:38:44 -0400 (EDT)
• References: <200906131001.GAA07123@smc.vnet.net>

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
>

• References:
  • Inverse / Laplace Transform Halved
    • From: Sid <pcoords29@gmail.com>