odd or even function Hello dear, I have a question in complex Fourier series: Q:/ how do I know whether the function is even or odd? if after solving: a$_0$ = 2$\pi$ a$_n$ = 0 b$_n$ = 2/$\pi$ C$_n$ = j/n C$_{n}$ = j/n Can you help me with that? 
Whether it's complex is irrelevant. Write the nth term (for nonzero n) in terms of sin and cos. For an odd function, the nonzero terms are all sin terms. For an even function, there are no nonzero sin terms. 
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The "$\displaystyle a_n$" terms are the coefficients of cos(nx) and the "$\displaystyle b_n$" terms are coefficients of sin(nx). Since cos(nx) is an even function, for all n, and sin(nx) is an odd function, for all n, a Fourier series is "odd" if and only if "$\displaystyle b_n= 0$" for all n and "even" if and only if "$\displaystyle a_n= 0$" for all n. We can also write a Fourier series as $\displaystyle \sum_{n=\infty}^\infty C_ne^{inx}$. Since $\displaystyle e^{inx}= \cos(nx)+ j \sin(nx)$, $\displaystyle \cos(nx)= \cos(nx)$ and $\displaystyle \sin(nx)= \sin(nx)$, that reduces to the previous case. 
Isn't that the wrong way round? 
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and my function is this function: $$ I(t)= \pi + \sum_{n=\infty}^\infty \frac j n e^{jnt} $$ with the following given data: $$ C_o=\pi $$ $$ \frac {ao} 2 = \pi $$ $$ C_n=\frac j n $$ $$C_{n}= \frac {j} n $$ $$ a_n=0 $$ $$ b_n=\frac {2} n $$ and the solutions said it is neither odd nor even and I want to know why it is neither odd nor even ..... 
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