My Math Forum (http://mymathforum.com/math-forums.php)
-   Complex Analysis (http://mymathforum.com/complex-analysis/)
-   -   odd or even function (http://mymathforum.com/complex-analysis/341585-odd-even-function.html)

 aows61 August 27th, 2017 01:17 PM

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?

 skipjack August 27th, 2017 05:05 PM

Whether it's complex is irrelevant. Write the nth term (for non-zero n) in terms of sin and cos. For an odd function, the non-zero terms are all sin terms. For an even function, there are no non-zero sin terms.

 aows61 August 28th, 2017 01:35 AM

clarify

Quote:
 Originally Posted by skipjack (Post 578901) Whether it's complex is irrelevant. Write the nth term (for non-zero n) in terms of sin and cos. For an odd function, the non-zero terms are all sin terms. For an even function, there are no non-zero sin terms.
Hello Dear,
can you clarify more ?

 Joppy August 28th, 2017 02:50 AM

Quote:
 Originally Posted by aows61 (Post 578931) Hello Dear,
Something is not quite right here :lol:

 aows61 August 28th, 2017 02:54 AM

Quote:
 Originally Posted by Joppy (Post 578934) Something is not quite right here :lol:
Hello Dear,

 Joppy August 28th, 2017 03:02 AM

Quote:
 Originally Posted by aows61 (Post 578935) Hello Dear, can you share your answer?
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! :lol:.

 aows61 August 28th, 2017 05:52 AM

Quote:
 Originally Posted by Joppy (Post 578936) 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! :lol:.
thanks for notifying and sharing this info with us,
if you have more info regarding the question, kindly share it with us...

regards,

 Country Boy August 28th, 2017 05:56 AM

Quote:
 Originally Posted by aows61 (Post 578886) 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?
You seem confused as to what a "Fourier series" is. The "$\displaystyle a_n, b_n$ and "$\displaystyle C_n, C_{-n}$" are different notations. We can write a Fourier series as $\displaystyle a_0+ a_1 \cos(x)+ b_1 \sin(x)+ a_2\cos(2x)+ b_2\sin(2x)+ \cdot\cdot\cdot$
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.

 skipjack August 28th, 2017 06:22 AM

Isn't that the wrong way round?

 aows61 August 28th, 2017 07:33 AM

thanks

Quote:
 Originally Posted by Country Boy (Post 578949) You seem confused as to what a "Fourier series" is. The "$\displaystyle a_n, b_n$ and "$\displaystyle C_n, C_{-n}$" are different notations. We can write a Fourier series as $\displaystyle a_0+ a_1 \cos(x)+ b_1 \sin(x)+ a_2\cos(2x)+ b_2\sin(2x)+ \cdot\cdot\cdot$ 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.
I think you mean odd if a_n = 0.

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 .....

All times are GMT -8. The time now is 08:03 AM.