# Fourier method | eigenfunctions

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• December 18th 2009, 08:11 PM
kingwinner
Fourier method | eigenfunctions
http://sites.google.com/site/asdfasdf23135/004.JPG

[note: also under discussion in sos math cyberboard]
• December 19th 2009, 04:42 AM
HallsofIvy
Quote:

Originally Posted by kingwinner
http://sites.google.com/site/asdfasdf23135/004.JPG

[note: also under discussion in sos math cyberboard]

$sin((n+1/2)(-\pi))= -1 = - sin((n+1/2)\pi)$ and
$(n+1/2)cos((n+1/2)(-\pi))= 0 = - sin((n+1/2)\pi)$ so sin((n+1/2)x) satisfies both $u(-\pi)= -u(\pi)$ and $u_x(-\pi)= -u_x(\pi)$. Yes, of course, they are eigenfunctions.