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MathGroup Archive 2001

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Re: Summation Formulae Table

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28447] Re: Summation Formulae Table
  • From: "Paul Lutus" <nospam at nosite.com>
  • Date: Thu, 19 Apr 2001 03:26:35 -0400 (EDT)
  • References: <9bjg2v$gs8@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"O D" <O_member at newsranger.com> wrote in message
news:9bjg2v$gs8 at smc.vnet.net...
> Is there a way to access the tables that Sum[] uses to simplify summations
into
> known functions like for example
>
> Sum[Exp[-a* n^2], {n, -Infinity, Infinity}]
>
> is simplified into
>
> EllipticTheta[3, 0, E^(-a)]

This simplification does not use a table, it uses a deterministic algorithm.

>
> Is there a way to use the table in reverse, to approximate a known
function?

You need to offer a specific example of a problem and a Mathematica solution
that you would like to see in a different form. Also, if you are interested
in approximating functions, you may want to approach the problem
differently, using regression methods such as are offered by "Fit" and
related resources.

--
Paul Lutus
www.arachnoid.com





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