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Jan
20
asked Parseval's Identity, problem with $|a_n|^2$
Jan
20
revised Fourier Series: even extension and Parseval Identity
added 51 characters in body
Jan
20
comment Fourier Series: even extension and Parseval Identity
@AlexR, please, not to be rude. That integral is very stupid, I have linked the WA result to say: "ehy, the result is correct!"
Jan
20
comment Fourier Series: even extension and Parseval Identity
@AlexR $a_n= \frac{2}{\sqrt \pi}\int_{0}^{\pi} (\pi-x)\cos nx dx$; "$a_0$ is wrong".. is wrong the formula or the result? (wolframalpha.com/input/?i=%28pi+-+x%29+integrate+from+-pi+to+pi)
Jan
20
comment Fourier Series: even extension and Parseval Identity
@AlexR I'm sorry but it was told me that if $$\bar{f}(x)=\begin{cases} f(x), x\in [0, L]\\ f(-x), x\in[-L, 0) \end{cases}$$, the expression of the $a_n$ is the one I wrote in the question...
Jan
20
comment Fourier Series: even extension and Parseval Identity
@AlexR, I know the meaning of "even".. f(x) is given by $f(x)=\pi-x$. I have to DO the even extension.. I haven't written in the question the funcion extended, because I thought that it wasn't important for the development of the exercise.. but if I have made a mistake, please, explain me why... thanks!
Jan
20
comment Fourier Series: even extension and Parseval Identity
@AlexR $f(x)=\pi -x$, then we have to consider its even extension.. (that, obviously, isn't f(x))
Jan
20
asked Fourier Series: even extension and Parseval Identity
Jan
3
accepted Contour integration of $\int_{-\infty}^{\infty}\frac {\sin^3 x}{x^3} dx$: where are the singularities?
Jan
3
awarded  Teacher
Jan
2
comment Contour integration of $\int_{-\infty}^{\infty}\frac {\sin^3 x}{x^3} dx$: where are the singularities?
@DanielFischer I have just written an answer, I'll be glad if you read it! :) Have a nice day!
Jan
2
answered Contour integration of $\int_{-\infty}^{\infty}\frac {\sin^3 x}{x^3} dx$: where are the singularities?
Jan
2
comment Contour integration of $\int_{-\infty}^{\infty}\frac {\sin^3 x}{x^3} dx$: where are the singularities?
@dustin I'm sorry! I'll do it this afternoon, at the moment I'm not at home! Have a nice day!
Dec
30
comment Limit with complex numbers
Thanks for your explanation!
Dec
30
comment Limit with complex numbers
So I want to prove that the function that I have posted in the question goes to zero for z->infinity. To answer to the question that you posted in your comment,I'd say that z is real.. am I wrong? Many thanks!
Dec
30
comment Limit with complex numbers
Thanks for your answer. I'm tryng to calculate $ \int_{-\infty}^{+\infty}\frac{ \sin^3}{x^3} \,dx$ with x=real variable. It was told me that I have to consider it as a particular case of the complex case. Than, I have expressed the sinus in the exponential form and tryed to close the path to apply the residue theorem.. But it was told me that I can apply it only if the limit (for z->infinity) of the function that I want to integrate is 0....
Dec
30
comment Limit with complex numbers
@MikeMiller something..
Dec
30
asked Limit with complex numbers
Nov
6
comment Contour integration of $\int_{-\infty}^{\infty}\frac {\sin^3 x}{x^3} dx$: where are the singularities?
@DanielFischer oh, thank you!!! If you write a little answer, I'll be happy to give you the "accepted answer" :)
Nov
6
comment Contour integration of $\int_{-\infty}^{\infty}\frac {\sin^3 x}{x^3} dx$: where are the singularities?
@RonGordon many thanks for your comment!! I'm going to read carefully your link tomorrow morning.. now it's too late.. thanks again!