August 27th, 2017, 02:17 PM  #1 
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  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? Last edited by skipjack; August 27th, 2017 at 05:40 PM. 
August 27th, 2017, 06:05 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,154 Thanks: 1422 
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.

August 28th, 2017, 02:35 AM  #3 
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  clarify 
August 28th, 2017, 03:50 AM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,410 Thanks: 481 Math Focus: Yet to find out.  
August 28th, 2017, 03:54 AM  #5 
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  share answer 
August 28th, 2017, 04:02 AM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,410 Thanks: 481 Math Focus: Yet to find out.  Sorry, i was actually referring to your use of the word 'dear'. Typically we use it when writing a formal letter. For example, "Dear aows61, how are you today?". However use of 'dear' in the context here ('hello dear') refers to the other meaning of the word: "regarded with deep affection". One might engage with ones lover by saying "hello dear". I like skipjack too, but not that much! . 
August 28th, 2017, 06:52 AM  #7  
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  Quote:
if you have more info regarding the question, kindly share it with us... regards,  
August 28th, 2017, 06:56 AM  #8  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,823 Thanks: 752  Quote:
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. Last edited by skipjack; August 28th, 2017 at 07:18 AM.  
August 28th, 2017, 07:22 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 18,154 Thanks: 1422 
Isn't that the wrong way round?

August 28th, 2017, 08:33 AM  #10  
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  thanks Quote:
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 ..... Last edited by skipjack; October 8th, 2017 at 05:09 AM.  

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