       Re: problem with Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg100684] Re: problem with Sum
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Thu, 11 Jun 2009 07:06:59 -0400 (EDT)

```On 6/10/09 at 5:31 AM, olfa.mraihi at yahoo.fr (olfa) wrote:

>I have this input: Sum[a[k], {k, 1, j}] - Sum[a[k], {k, 1, i+j-n}]
>How it is possible to let mathematica gives as output: Sum[a[k], {k,
>i+j-n+1, j}] if i+j-n<j and Sum[a[k], {k, j+1, i+j-n}] if i+j-n>j

Have you looked at the documentation for If? Specifically,

If[i<n, Sum[a[k], {k, 1, i+j-n}], Sum[a[k], {k, j+1, i+j-n}]]

here, I've simplified your i+j-n < j to the equivalent i < n.

Or perhaps you are asking how to transform

Sum[a[k], {k, 1, j}] - Sum[a[k], {k, 1, i+j-n}]

to say

Sum[a[k], {k, 1, i+j-n}]

That can be done using pattern matching with a replacement rule.
That is:

In:= x = Sum[a[k], {k, 1, j}] - Sum[a[k], {k, 1, i + j - n}]

Out= Sum[a[k], {k, 1, j}] - Sum[a[k], {k, 1, i + j - n}]

In:= First[x] /. j -> i + j - n

Out= Sum[a[k], {k, 1, i + j - n}]

```

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