       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)

```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

```

• Prev by Date: Re: Locator appearance
• Next by Date: Where is the code for DistanceMatrix?
• Previous by thread: Re: integrate log*sinc
• Next by thread: Where is the code for DistanceMatrix?