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MathGroup Archive 2001

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Re: Summation Formulae Table

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28472] Re: Summation Formulae Table
  • From: O <O_member at newsranger.com>
  • Date: Fri, 20 Apr 2001 04:24:20 -0400 (EDT)
  • Organization: http://www.newsranger.com
  • References: <9bjg2v$gs8@smc.vnet.net> <9bm4pg$j2k@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Paul,
thank you for your attempt to answer my question, I am sure I am not forming it
right.
Let me try once again, maybe this time I can do better.

Where or how can I find the list of patterns and rewrite rules that built-in
mathematical functions like 
Exp and Zeta and others will match against?

In[1]:= Sum[1/k^p,{k,1,Infinity}]

Out[1]= Zeta[p]

In[17]:= Sum[x^k/k!,{k,0,Infinity}]

Out[17]= Exp[x]

How can I see the definitions of built-in mathematical functions or the rules
they are associated with?
UpValues[] and DownValues[] return empty lists. 

Thanks again,
O


In article <9bm4pg$j2k at smc.vnet.net>, Paul Lutus says...
>
>"O D" <O_member at newsranger.com> wrote in message
>news:9bjg2v$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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