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Convolve: Different Looking Results. (2)
Posted:
Apr 26, 2013 11:08 PM


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



