Integrals of Fourier Series

• Subject: [mg3179] Integrals of Fourier Series
• From: goster at nature.Berkeley.EDU (George Oster)
• Date: 14 Feb 1996 03:57:48 -0600
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• Organization: Wolfram Research, Inc.
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```Suppose I want to substitue a Fourier Series into an integral:

u[x_] := Sum[A[n] Sin[n Pi x/L], {n, 1, Infinity}]

Integrate[(u''[x])^2, {x, 0, L}]

This has an easy analytical solution that I can't get Mma to find, because
Mma doesn't know that Sum and Integrate commute, and that Sin[n
Pi] = 0 for all integer n.

How to do this?

GO

_____________________________________________
Professor George Oster
University of California
201 Wellman Hall
Berkeley, CA 94720-3112
Phone & Fax: 510-642-5277
Email: goster at nature.berkeley.edu
http://www.cnr.berkeley.edu/~goster/home.html

```

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