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MathGroup Archive 2004

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Bug? Wrong result from infinite sum.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49615] Bug? Wrong result from infinite sum.
  • From: Ben <serpent11 at hotmail.com>
  • Date: Sat, 24 Jul 2004 03:48:36 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I'm trying to get Mathematica to evaluate Poisson brackets for me, but
I am encountering a problem where the sum returns the wrong number.
Try this:

In a new notebook, evaluate:

the partial derivative with respect to a[2] of a[1] (returns 0)

the partial derivative with respect to a[2] of a[2] (returns 1)

the partial derivative with respect to a[2] of a[infinity] (returns 0)

the sum from n = 1 to 1000 of the derivative with respect to a[2] of
a[n] (returns 1)

the sum from n = 1 to infinity of the derivative with respect to a[2]
of a[n] 

This final sum returns 0 in Mathematica 4.1, and in Mathematica 5.0,
it raises an error, indeterminate expression encountered.  If I
instead take the limit of the sum from n = 1 to m of the derivative
with respect to a[2] of a[n], I get zero regardless of the value I let
m approach.

Can anyone suggest a workaround or fix for this problem?  It could be
a bug with Mathematica, or could be that I am doing something
technically wrong.

Thanks,
~Ben


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