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Topic: Convolve: Different Looking Results. (2)
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Posts: 16
Registered: 9/24/08
Convolve: Different Looking Results. (2)
Posted: Apr 26, 2013 11:08 PM
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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

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.


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