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Convolve: Different Looking Results. (2)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130623] Convolve: Different Looking Results. (2)
  • From: Polar Coords <pcoords29 at gmail.com>
  • Date: Fri, 26 Apr 2013 23:08:37 -0400 (EDT)
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Dear Mathgroup,

Sorry about my last incomplete mail.

Consider the following in Mathematica 8 (  It's a convolution as in Laplace
transforms)

In[15]:= Convolve[Exp[-x] UnitStep[x], Sin[2 x] UnitStep[x], x, y,
 Assumptions -> y > 0]

Out[15]= -(2/5) (Cos[2 y] - Cosh[y] - Cos[y] Sin[y] + Sinh[y])

Now , use t instead of y

In[16]:= Convolve[Exp[-x] UnitStep[x], Sin[2 x] UnitStep[x], x, t,
 Assumptions -> t > 0]

Out[16]= 1/5 (2 E^-t - 2 Cos[2 t] + Sin[2 t])


They're equivalent, but why the different looking results?  We have the
Out[16] results if we use symbols a to w, but as in Out[15] if using   y
or  z !

Do members have the same results in Mathematica 9?

Finally, on a lighter note, one usually convolves 2 functions of x to get a third function of x.  I can't suss out why Mathematica gives the answer in terms of
a new variable.

So, if I want to convolve 2 output functions of t, then I need to change to
another variable and tell it to give the answer in terms of t.  A hassle.

Thanks for your help.
Cheers.

Sid




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