gauss mouse
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I'm trying to show that the Fourier series of f(x)=x^2 converges and I can't. Does anybody know if it actually does converge? (I'm assuming that f(x)=x^2 for x\in [-\pi,\pi]).
The Fourier Series itself is \displaystyle\frac{\pi^2}{3}+4\sum_{n=1}^\infty \frac{(-1)^n}{n^2}\cos nx
I tried using Dirichlet's test but it wasn't working for me, though that may be because I'm doing something wrong.
The Fourier Series itself is \displaystyle\frac{\pi^2}{3}+4\sum_{n=1}^\infty \frac{(-1)^n}{n^2}\cos nx
I tried using Dirichlet's test but it wasn't working for me, though that may be because I'm doing something wrong.