       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:= InverseLaplaceTransform[LaplaceTransform[BesselI[1, t], t, s], s, t]
Out= 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:= LaplaceTransform[InverseLaplaceTransform[s*Exp[(-a)*Sqrt[s]], s, t], t, s]
Out= 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 ?
>
>