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Re: Using "Limit" when the limit is a delta function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85239] Re: Using "Limit" when the limit is a delta function
  • From: Jim Rockford <jim.rockford1 at gmail.com>
  • Date: Mon, 4 Feb 2008 03:07:11 -0500 (EST)
  • References: <fnuhi4$9te$1@smc.vnet.net> <fo1994$fm5$1@smc.vnet.net>

On Feb 2, 3:23 am, "D. Grady" <D.C.Gr... at gmail.com> wrote:
> Mathematica tries to make as few assumptions as possible about
> undetermined parameters in an expression like this.  So, while in your
> head you're probably thinking that D should be a positive real number,
> Mathematica is thinking that D could be any random complex number.
> The same goes for x.  You can specify assumptions like this using
> Assuming:
>
> Assuming[{x \[Element] Reals, d \[Element] Reals, d > 0},
>  Limit[1/Sqrt[4 \[Pi] d t] Exp[-x^2/(4 d t)], t -> 0]]


Hey Daniel -- some of the tips you provide on adding Assumptions and
so forth are valuable.  Much thanks.

As for distributions, it would not be hard for Mathematica to build in
to its repertoire a few well known function families that have well
known limiting distributions (such as the DiracDelta).  They already
do this, in a sense, through their recognition that a derivative of a
Heaviside (step) function is a Delta function.  They simply haven't
incorporated this yet.  I guess the interest just isn't there.

Thanks again.
Jim


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