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Re: Dealing with sums

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41167] Re: Dealing with sums
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Tue, 6 May 2003 06:01:05 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <b8g114$pg5$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <b8g114$pg5$1 at smc.vnet.net>,
 Stepan Yakovenko <yakovenko at ngs.ru> wrote:

>   I want to get a derivative in terms of KroneckerDelta function:
> 
>   \!\(\[PartialD]\_\(a\_3\)\(\[Sum]\+\(i = 0\)\%N a\_i\)\)
> 
>   But I get 0.
>   
>   Is there a way to do it in Mathematica ?

In many situations, the summation symbol is not intended to imply 
explicit summation but is just a notational device: the Einstein 
summation convention, where summation over repeated indices is implied 
rather than explicitly stated, e.g., 

  \!\(TraditionalForm\`\(\(\[Sum]\+\(i = 1\)\%n\( a\_i\) b\^i \[Rule]   
  \(a\_i\)       b\^i\)\(,\)\)\) 

can often be used to simplify the algebra. Interestingly, this 
convention translates into a general principle for analyzing and 
evaluating integrals and products of sums in Mathematica -- just focus 
on the summand (i.e., the general term of the sum) and drop the 
summation symbol. 

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul



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