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Re: Re: simplifying inside sum, Mathematica 5.1

On 26 Jan 2005, at 18:14, Richard Fateman wrote:
> As for Andrzej's comment, that this does the job...
> Block[{Power,Infinity},
>     0^(i_) := KroneckerDelta[i, 0]; Sum[a[i]*x^i, {i, 0, Infinity}]/. x
> -> 0]
> Here are some comments:
> 1. There is no need for Infinity to be bound inside the Block.

Indeed, I did not check that. I had reasons to think it was needed.

> 4. Your solution gives the wrong answer for
> Sum[a[i]*x^i, {i, -1, Infinity}]

Since any sum can be split into a finite sum over the negative indices 
and an infinite sum over indices >=0 and since finite sums are handled 
correctly this is essentially a cosmetic issue. In fact it is easy to 
modify Sum to automatically split all sums in this way, and to use the 
Block trick for the infinite part. But I don't think this is important 
enough to bother.

> It also doesn't work for
> Sum[a[i]*x^(i^2), {i, -1, Infinity}]
> This latter problem suggests an inadequacy in the treatment of the
> simplification of   Sum[KroneckerDelta[...]....]

Well, yes. One can always find ways to trip up Mathematica (and all 
other CAS) in this sort of thing. It's a bit like playing chess with a 
computer program; however strong it is if you get to know it well 
enough you will find ways to beat it (assuming of course you are a good 
chess player and understand computers). But the difference is that CAS 
is not meant to be your opponent and trying to trip it up (which is 
also what most of Maxim's examples involve) is a pointless exercise, 
which may amuse people who like such things but has nothing to do with 
any serious work.

Andrzej Kozlowski

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