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MathGroup Archive 2001

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Re: KroneckerDelta in sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31687] Re: [mg31675] KroneckerDelta in sum
  • From: BobHanlon at aol.com
  • Date: Sat, 24 Nov 2001 16:44:00 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/11/23 8:25:10 AM, 
reichelt at ax1348.physik.uni-marburg.de writes:

>I guess I have a rather simple problem. If I write
>Sum[a[i, j]KroneckerDelta[i - j], {i, -Infinity, Infinity}]
>
>Mathematica answers
>a[j, j]
>
>Now, if I use a two-fold sum
>Sum[a[i, j]KroneckerDelta[i - j], {i, -Infinity, Infinity}, {j, -Infinity,
>
>    Infinity}]
>
>the expression is not simplified.
>How can I force Mathematica to give results like
>Sum[a[j,j],{j,-Infinity, Infinity}]
>

Sum has the attribute HoldAll

Attributes[Sum]

{HoldAll, Protected, ReadProtected}

Either, manually separate the sums

Sum[Evaluate[Sum[a[i,j]KroneckerDelta[i-j],
      {j,-Infinity,Infinity}]], 
  {i, -Infinity, Infinity}]

Sum[a[i, i], {i, -Infinity, 
   Infinity}]

or use a replacement rule to separate the sums

Off[Sum::itform];

Sum[a[i,j]KroneckerDelta[i-j],
    {i,-Infinity,Infinity},
    {j,-Infinity,Infinity}] /. 
  Sum[expr_, iter1_, iter2_] :> 
    Sum[
      Evaluate[Sum[expr, iter2]], iter1]

Sum[a[i, i], {i, -Infinity, 
   Infinity}]

Note that with Sum, multiple iterators are listed from the outside in.


Bob Hanlon
Chantilly, VA  USA


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