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MathGroup Archive 2001

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Re: Summation Formulae Table

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28440] Re: Summation Formulae Table
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 19 Apr 2001 03:26:28 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <9bjg2v$gs8@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

no, because Mathematica use different series expansions
with different expansion points. You may choose a expansion
point with nonzero connvergence radius and use a Taylor/Laurent
of Frobenuis expansion depending on the function. 
The best way is to look into the standard books like
Abromovitz/Stegun

Regards
  Jens

O D wrote:
> 
> 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)]
> 
> Is there a way to use the table in reverse, to approximate a known function?
> 
> I am not interested in the above example, so please do not tell me how I can
> approximate EllipticTheta[]...
> 
> I am a rather naive Mathematica user, so please be explicit.
> 
> Thank you.
> O


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