Convolve: Different Looking Results. (2)
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- 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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