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DiscreteDelta Evaluation Question

• To: mathgroup at smc.vnet.net
• Subject: [mg49770] DiscreteDelta Evaluation Question
• From: Ben <serpent11 at hotmail.com>
• Date: Fri, 30 Jul 2004 06:02:22 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi:

In evaluating Poisson brackets, I've gotten Mathematica to simplify
the brackets down to an infinite sum of deltafunctions, but though the
sum should be very easy to evaluate, I can't convince it to simplify
it.  Here's a typical case that it won't simplify:

Sum[(-Sqrt[-2] indx DiscreteDelta[2 - indx] - 
          0.5 Sqrt[-1] DiscreteDelta[indx] DiscreteDelta[
              2 - indx])((1 - Sqrt[2]) DiscreteDelta[indx]
DiscreteDelta[
              2 - indx] + 
          Sqrt[2] DiscreteDelta[2 - indx]) - (Sqrt[-2] indx
DiscreteDelta[
              2 - indx] + 
          0.5 Sqrt[-1] DiscreteDelta[indx] DiscreteDelta[
              2 - indx])((1 - Sqrt[2]) DiscreteDelta[indx]
DiscreteDelta[
              2 - indx] + Sqrt[2] DiscreteDelta[2 - indx]), {indx, 1, 
    Infinity}]

You can cut and paste it into a notebook.

I've tried 

Unprotect[DiscreteDelta, Times];

DiscreteDelta[i_] * DiscreteDelta[i_] := DiscreteDelta[i];

Protect[DiscreteDelta, Times];

but it still won't evaluate this seemingly simple expression.

Any advice would be greatly appreciated.

Thanks,
~Ben