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Symbolic Integration of Sums

• To: mathgroup at smc.vnet.net
• Subject: [mg79129] Symbolic Integration of Sums
• From: Peter <pjcrosbie at gmail.com>
• Date: Thu, 19 Jul 2007 03:33:05 -0400 (EDT)

I am having trouble figuring out how to Mathematica to recognize sums when I
take derivates.

Here is a very simple example, define

portM = Sum[w[i] m[i], {i, 1, n}]

Then, if I try to take the derivative of portM wrt say w[1] I get 0
instead of m[1].

D[portM, w[1]] --> returns 0

If I spell the sum out explicitly using say for n=10:

portM = Sum[w[i] m[i], {i, 1, 10}]

I get the correct answer but this is often messy with the real
problems I am working with and it also removes the ability to work
with the length of sum in the other parts of the analysis I am doing.

Is using Sum in this way simply a level of abstraction more than Mathematica
can do or am I asking it the wrong question?

Many thanks.

• Follow-Ups:
  • Re: Symbolic Integration of Sums
    • From: Carl Woll <carlw@wolfram.com>