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Re: delta function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89957] Re: delta function
  • From: Roman <rschmied at gmail.com>
  • Date: Wed, 25 Jun 2008 06:26:49 -0400 (EDT)
  • References: <g3ihpo$fdt$1@smc.vnet.net>

Magician,
I don't know an answer to your question; however, the function with
the proper limit is
  Exp[-(x-xo)^2/t]/Sqrt[Pi*t]
and not the one you specify. You can check this with
  Integrate[Exp[-(x-xo)^2/t]/Sqrt[Pi*t], {x,-Infinity,Infinity},
Assumptions -> t>0]
which gives you 1 for all values of t; this is what the Dirac delta-
function requires.
Roman.


On Jun 21, 11:31 am, Magician <jadoo.d... at gmail.com> wrote:
> I am integrating over a function (not written in mathematica syntax)
>
> u=F(x)   e^(-  (x-xo)^2/t  ) /t  ,
> i know in the limit t ->0,  e^(-  (x-xo)^2/t  ) /t = delta(x-xo), but
> how do i get mathematica to recognize this.
>
> In mathematica, how can i construct hings like the Sokhotskyi-Plemelj
> formula ?



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