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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

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

**Follow-Ups**:**Re: Convolve: Different Looking Results. (2)***From:*Bob Hanlon <hanlonr357@gmail.com>