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MathGroup Archive 2005

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Re: Infinite sum of gaussians

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56105] Re: Infinite sum of gaussians
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Fri, 15 Apr 2005 04:48:11 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 4/14/05 at 8:54 AM, astanoff at yahoo.fr (Valeri Astanoff) wrote:

>I'm not a mathematician, just an engineer, and what puzzles me is
>this
>:

>In[1]:=
>{ Sum[Exp[-(z-k)^2/2], {k, -Infinity, Infinity}],
>      Sqrt[2*Pi]+
>        Cos[2*Pi*z]*(EllipticTheta[3,0,1/Sqrt[E]]-Sqrt[2*Pi])} /. z ->
>1/2 //
>  N[#,35]&

>Out[1]=
>{2.5066282612190954600008515157581306,
> 2.5066282612190954600008515157581301}

>If I trust mathematica, this should induce to think the equality is
>false.

I also trust Mathematica for the most part. But the results you obtained do not show the equality to be false or show a problem with Mathematica. For any numerical result there are limitations as to the precision of any computed result. Different methods using the same numerical precision at every step can and will arrive at somewhat different answers. These two results differ only in the last digit and should be regarded as the same in view of unavoidable issues with numerical computation.
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