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