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I need help finding the Fourier coefficients of:

$f(x) =\begin{cases} \sum_{n=0}^\infty{\frac{e^{inx}}{1+n^2}} & \text{if } x\neq 2k\pi \\0& \text{if } x= 2k\pi \end{cases}$

And my main problem is that I know how to find the coefficients for each case separately, but how do I reach a final answer for the whole function?

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    The answer is before your eyes.2012-08-29
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    yes i know that it is already in the form of it's Fourier series for $x\neq 2k\pi$ but, as i originally stated, my problem is how to show that the coefficients are $\frac{1}{1+n^2}$ for the entire function $f$.2012-08-29

2 Answers 2