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Re: Strange Laplace Transform in 6.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81766] Re: [mg81735] Strange Laplace Transform in 6.0
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Wed, 3 Oct 2007 02:28:52 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200710020944.FAA28804@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

For

   f[x_]:=Exp[x^2] Exp[a x]

clearly the issue is for which values of the parameter a (and then for 
which values of the variable s) the indefinite integral

   Integrate[Exp[-s x] f[x],{x,0,\[Infinity]}]

converges.

I don't have further insight into what's going on in version 6 vs. 
version 5.2, but I did try to check the result in two other major 
competitors to Mathematica.

In one, the Laplace transform was returned unevaluated, with no conditions.

The other said it did not recognize the transform function, and I 
learned that one had to purchase a separate symbolic add-on package even 
to try to evaluate the transform.

C. Seja wrote:
> Hi,
> 
> just have a look at this:
> 
> Mathematica 5.2:
> 
> In[3]:=
>  LaplaceTransform[Exp[x^2]*Exp[a*x],x,s]
> 
> Out[3]=
> \!\(1\/2\ \[ExponentialE]\^\(\(-\(1\/4\)\)\ \((a - s)\)\^2\)\ \@?\ 
> Erfi[1\/2\ \
> \((\(-a\) + s)\)]\)
> 
> 
> Mathematica 6.0:
> 
> In[1]:= LaplaceTransform[Exp[x^2]*Exp[a*x], x, s]
> Out[1]= \[ExponentialE]^x^2/(-a + s)
> 
> 
> Why does 6.0 give this result? Am I missing something?
> 
> 
> 
> Regards,
> 
> C. Seja
> 
> 
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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