Re: Assuming and Integrate

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• Subject: [mg128328] Re: Assuming and Integrate
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 7 Oct 2012 01:31:55 -0400 (EDT)
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```How to treat exceptional cases, here m = n an integer, is always an issue with Integrate (and other operations). Here one would hope to see at least a ConditionalExpression for the general situation Element[{n,m}, Integers]. After all, such integrals are so common in Fourier analysis.

Perhaps this should even be reported as a bug to Wolfram Research.

On Oct 6, 2012, at 1:53 AM, hamiltoncycle at gmail.com wrote:

> When I try the line below in Mathematica 8 I get the answer 0 which is what I expect when m and n are different but not when m=n. Can anyone explain how to do this correctly?
>
> Assuming[Element[{n, m}, Integers], Integrate[Sin[n*x]*Sin[m*x], {x, 0, Pi}]]
>
> When m=n we should get Pi/2, as in this case:
>
> Assuming[Element[n, Integers], Integrate[Sin[n*x]*Sin[n*x], {x, 0, Pi}]]
>

---
Murray Eisenberg
murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                  413 545-2859 (W)
710 North Pleasant Street                      fax   413 545-1801
Amherst, MA 01003-9305

```

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