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
- References:
- Strange Laplace Transform in 6.0
- From: "C. Seja" <p5secr2@uni-jena.de>
- Strange Laplace Transform in 6.0