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Laplace transform of periodic function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109180] Laplace transform of periodic function
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 16 Apr 2010 05:50:01 -0400 (EDT)
  • Reply-to: murray at math.umass.edu

Is there some way to tell Mathematica that a function is periodic when 
using LaplaceTransform to calculate its transform?

For example, if I define...

   f[t_ /; 0 <= t < 1] :=
       t - UnitStep[t - 1/2] t + UnitStep[t - 1/2] (1 - t)
   f[t_] := f[t-1]

... and then try

   LaplaceTransform[f[t], t, s]

... I get an $IterationLimit error.

Of course I can apply a standard formula to obtain the result:

   f[t_] :=
       t - UnitStep[t - 1/2] t + UnitStep[t - 1/2] (1 - t)

   transformf[s_]=Integrate[Exp[-s t]f[t],{t,0,1}]/(1-Exp[-s])

But surely there's some way to force Mathematica to give the result of 
the preceding through direct use of LaplaceTransform?

-- 
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


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