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Re: Inverse / Laplace Transform Halved

• To: mathgroup at smc.vnet.net
• Subject: [mg100793] Re: [mg100753] Inverse / Laplace Transform Halved
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 14 Jun 2009 05:39:31 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200906131001.GAA07123@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Mathematica 7.0.1:


   InverseLaplaceTransform[LaplaceTransform[BesselI[1,t],t,s],s,t]//
       Simplify // InputForm
Piecewise[{{BesselI[1, t]/2, s > 1}, {-DiracDelta[t], s < 1}}, 0]

   LaplaceTransform[InverseLaplaceTransform[s*Exp[(-a)*Sqrt[s]],s,t],t,s]
          // InputForm
s/E^(a*Sqrt[s])

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
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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