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Topic review (newest first)

bobbym
2013-05-22 20:06:32

Hi;

Thanks for saying that but I rarely do a post where I do not learn something new and I meet people from other places.

clumsy shark
2013-05-22 20:03:14

^^ It's been a pleasure to know someone dedicated like You  ^_^

bobbym
2013-05-22 19:42:03

Egypt? Yes, I do but just from reading.

clumsy shark
2013-05-22 19:29:11

No , I'm from Egypt. Do you know it ?

bobbym
2013-05-22 19:12:13

What me get smarter? Fat chance of that happening. They say you can spit in one hand and wish in the other and watch which one will fills up faster.

Are you attending Jerome's classes?

clumsy shark
2013-05-22 19:07:49

Oh yea then it must be the second wink big_smile

bobbym
2013-05-22 18:32:17

Hi;

It is very confusing to me also. I do wish he was clearer or I was smarter.

clumsy shark
2013-05-22 18:30:53

Thank You bobbym ^_^ That was really such an annoying matter, I got it .. THANKS smile

bobbym
2013-05-22 09:49:09

I agree with all your complaints about

So the equality
is only in some sense of generalized functions.'

I have no idea what his vague wording means.

Let me check that series for correctness.


That is indeed a series that represents tan(x). The poor convergence he is talking about at the endpoints is caused by the well known Gibbs phenomena for Fourier series. The blue line is tan(x) and the red is a truncated form of his sum. That type of behaviour is standard for a Fourier fit.

The paper is from a lecturer at MIT.

He may be correct in his derivation too because your understanding of a Dirichlet condition might need some adjustment. There is an interesting discussion of that at

http://forum.allaboutcircuits.com/showt … hp?t=10266

it might help a little. From the viewpoint of a practical numerical analyst I would go with Kreyszigs definition which would just handle tan(x) as another piecewise function which are fit by Fourier series all the time.

Follow this link to 10.1.2

http://fractional-calculus.com/termwise … tive_1.pdf

To sum up that is only a Fourier series in some vague sense that no one is willing to share. Again, from a practical standpoint I accept the Fourier series of it but do not use such a garbage series for computation!

clumsy shark
2013-05-22 07:39:45

Thanks bobbym for replying smile

Well I can't get how he made this expansion ?? Is it allowed ? I see those two answers  contradicting yikes I understand well that tan(x) is unbounded at x = pi/2 and fourier series is only applicable to periodic functions where f (x) is defined for all real x
how could he manage it and what does his phrase 'This series has very poor convergence properties (look at x= pi/4). So the equality
is only in some sense of generalized functions.' means ??
I wanna know what misunderstanding I suffer here big_smile

sorry for my bad language
Thnx ^_^

bobbym
2013-05-22 05:21:03

Hi clumsy shark;

I am not following that well. You are right about the FourierSeries for tan(x). But what part of the derivation of that series has you stumped?

clumsy shark
2013-05-21 21:26:28

Which of fourier representations is suitable for f(x) = tan (x) : fourier trigonometric series, fourier half-range expansion , oe fourier integral and why ?

Well I searched and found that :
1-     tan x cannot be expanded as a Fourier series .Since tan x not satisfies Dirichlet’s   
       conditions.(tan x has infinite number of infinite discontinuous).
2- the pic (sorry posting links is not allowed for me )

the first answer is clear for me but I can't understand the pic I go confused :S

THNX in advance smile

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