Find the Fourier series of the function , with a period of , defined by

(Sorry, couldn't get the coding right to write it out properly).

I need a fairly lengthy explanation on this one 'cause I have no idea. Cheers.

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- April 26th 2010, 03:18 AMchella182Fourier series
*Find the Fourier series of the function , with a period of , defined by*

(Sorry, couldn't get the coding right to write it out properly).

I need a fairly lengthy explanation on this one 'cause I have no idea. Cheers. - April 26th 2010, 04:47 AMtonio

If you really have "no idea" about this then you better read/check your books/class notes. Nobody not having an idea of this should be trying this kind of problems.

It is my opinion that "fairly lengthy explanations" belong in the classroom or with a particular teacher. Here you can usually expect a little explanation and

some hints and/or complete resolution but without much explanation.

In this case it's hard to decide what you're supposed to know and thus how to approach this problem: have you studiedexponential__complex__

Fourier series? If that's the case, and since it seems to be that

, then we get that

.

Check the above and then evaluate (trivial integral)

Tonio - April 26th 2010, 04:51 AMchisigma
For a function of period is...

(1)

... where...

(2)

Remebering that for is...

(3)

... and for ...

(4)

... we obtain...

(5)

Kind regards

- April 26th 2010, 05:17 AMchella182
Thankyou chisigma for not getting condescending and helping :) exactly what I needed.

tonio, why bother replying if you think the way I'm asking for help isn't right, really? I appreciate that you're taking time out of your day to contribute, but I really don't appreciate your tone. The reason I say that I "don't have a clue" is so I don't get replies saying things like "Have you tried [such-and-such a method]?" because this area is by no means my speciality, so I most likely haven't or don't know what you're actually talking about.

I asked in the class and got a sub-standard explanation which didn't help much, AND I checked my notes and couldn't find how to do it in there (you really shouldn't be presuming that I haven't hcked my notes just 'cause I'm asking on here btw) so I turned to this site for help. If you can't or don't want to help, then don't. - April 26th 2010, 10:05 AMtonio

Thanx for the advice. From now on I won't ever try, but don't worry too much: as you can see, there may always be someone ready to do your whole work for you, eventhough what you asked is explained in all kinds of ways in thousands of internet sites. Of course, there are also thousands of books...(Nerd)

Tonio - April 28th 2010, 02:35 PMchisigma
The post opened by chella 182 is very 'suggestive' because it contains a little 'enigma'...

It has been demontrated that the function...

(1)

... can be expanded in Fourier series as...

(2)

All right!... now let's consider the derivative of (1)...

(3)

... and proceed to compute its Fourier coefficients...

(4)

... so that is...

(5)

The problem does arrive now: deriving in 'formal way' from (2) we obtain...

(6)

Because (5) and (6) seem 'a little conflictual' we are in front of two possibilities...

a) it has been some error from me [probably it is!...]

b) it holds the 'identity' [probably it isn't!...]

Kind regards