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Consider $f(t) = \frac{\pi - t}{2}$, $t \in [0, 2\pi]$

The complex fourier coefficients are $c_n = \frac{1}{2\pi}\int_0^{2\pi}\frac{\pi - t}{2}e^{-int}dt$

Which turns out to be $-\frac{i}{2n}$ if im correct.

When constructing the fourier series, what's the n=0 term supposed to be and why?

saldukoo
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    You can find $\hat f(0)$ from the definition. You made a slight error, or at least an oversight, in your previous calculation: You used $e^{-int}/(-in)$ as an antiderivative for $e^{-int}$. That's only valid for $n\ne 0$. – David C. Ullrich May 07 '16 at 16:13
  • @David C. Ullrich Right. That clears things up. – saldukoo May 07 '16 at 16:15

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You have $$ c_0=\frac1{2\pi}\int_0^{2\pi}\frac{\pi-t}2\,dt=\frac1{4\pi}\,\left(\pi\times2\pi-\frac{(2\pi)^2}2 \right) =0. $$

Martin Argerami
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