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can anybody show me the proof of fourier series?

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well i didnt find it anywhere, please help me with sites where to find the proof if u wont like typing.

well its easy to understand that if the rhs is true the lhs will be a periodic function for the lcm of the period remains same not the vice versa. plese give me the proof.

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I'm going to move this to one of the maths sub fora.


I'm not entirely sure this is in any way an easy task, IIRC it took about 100 years for anyone to sort out whether fourier was right in his nice little series...

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What exactly do you mean by proof? The proof that the series converges? Iirc, the series does not converge under all possible criteria for convergence. You should find something in any good calculus book (math for mathematicians at university level). In the unlikely case that you speak German you could use O. Forster: "Analysis 1".


EDIT: Or, seeing Klaynos' post, http://en.wikipedia.org/wiki/Convergence_of_Fourier_series

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no. i dont care whaether it converges or not, for the time being atleast. what i wanted to know really was that if say f(x) is a function of period 2pi. then y is it supposed to be able to be written as linear combinations of functions of sines & cosines their angles being multiples of 2pi always?


it's easy to understand the opposite way instead if there is a linear combination of sines & cosines of multiples of 2pi then the lcm of their periods become 2pi hence the combined function has the period 2pi.

but our books state the 1st one regarding shm as fourier series.


somebody please explain this i really didnt get it anywhere.

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