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From: Murray Eisenberg on 16 Apr 2010 05:49
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(a)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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