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Re: Inverse / Laplace Transform Halved

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100785] Re: [mg100753] Inverse / Laplace Transform Halved
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 14 Jun 2009 05:38:00 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

$Version

7.0 for Mac OS X x86 (64-bit) (February 19, 2009)

InverseLaplaceTransform[
  LaplaceTransform[
    BesselI[1, t], t, s] // Simplify,
  s, t] // Simplify

Piecewise[{{BesselI[1, t]/2, s > 1}, {-DiracDelta[t], s < 1}}]

However,

LaplaceTransform[
 InverseLaplaceTransform[
  BesselI[1, t], t, s], s, t]

BesselI[1, t]

No problem with second example

LaplaceTransform[
 InverseLaplaceTransform[
  s*Exp[(-a)*Sqrt[s]], s, t], t, s]

s/E^(a*Sqrt[s])


Bob Hanlon

---- Sid <pcoords29 at gmail.com> 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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