# Math Help - Fourier method | eigenfunctions

1. ## Fourier method | eigenfunctions

[note: also under discussion in sos math cyberboard]

2. Originally Posted by kingwinner

[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.