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Im Having some problems by calculating some Complex Form of Fourier Series.

I did it for $x$ and for $x^2$ with real numbers but now I´m trying to calculate de Fourier Series of $f(x)=x$ in $[- \pi , \pi ]$ but I'm stuck with operations with complex numbers.

Maybe you could help me.

I know the answer should be:

$ \sum_{n=1}^{\infty} {(-1)^n i e^{inx}}/{n} + \sum_{n=1}^{-\infty} {(-1)^n i e^{inx}}/{n} $

Thanks in advance!

alfonso
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  • HINT: Integrate by parts, just like you did in the real case. It is even easier now. Alternatively, you can just expand the exponential via Euler's formula, thus recovering the complex coefficients from the real ones. – Giuseppe Negro Feb 24 '15 at 21:55
  • What operation you are stuck with? You mean the integral $$\int_{-\pi}^{\pi} x e^{-inx} dx $$? – science Feb 24 '15 at 21:55
  • yeah I dont know how to calculate the $C_{n}$ – alfonso Feb 24 '15 at 22:01

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