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I'am a little confused. In my text book it is written that all odd function can be described by a sine series.

I have this following equation from an exercise:

$$A_{0}+\sum\limits_{n=1}^\infty \Big(A_{n} \cos(n \phi) + B_{n} \sin(n \phi)\Big)c^{n} = \sin\left(\frac{\phi}{2}\right)$$

It's a standard fourier series, where n and c is positive. Then it is written in the solution that $B_{n}c^{n} = 0$ because of symmetry reasons. I'am confused because then the fourier serie only have cosine term and the function on the right hand side is an odd function?!

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    You should indicate in which $\phi$-interval the equation is supposed to hold. It cannot be true for all real $\phi$.2012-12-24

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