Fourier Analysis 6: Fourier Series of x^2 [MAY NOT = f(x)]

[DasGewitter83]

I would get crazy if I had to listen to him more.....talking so fast that it is almost imposible to follow....very bad teacher...

[JonnyHackerRed]

Good energy and skill, thanks for sharing.

[pietersmulders]

I spend some time tryin' to find the series in -pi, pi, and I think I found it, but because I'm belgian, I couldn't quite understand if you say it is impossible, or that we simply can not know if it is correct. According to me, the series for -pi, pi equals:

pi²/3-4cos x+cos 2x -4/9 cos 3x + 1/4 cos 4x -4/25 cos 5x + 1/9 cos 6x -4/49 cos 7x+ ...

Thanks for your help.

[wadud88]

@pietersmulders

Yes this series is correct.

[NeRvExNaTiOn]

Its funny cuz hes asian

[obrebel4ever02]

what if the limit was 1<x<3???

[spectrex1]

What is it that you've done at 2:00? i don't understand how you've computed that integral.

[theYusrie]

Thanks... :)

[matBTF]

what the hell am i watchin man

crazy shit

[tharock220]

Ugh, thanks for the help. I just hate having to integrate by parts over and over on exams.

[2BobSaget3]

Assuming convergence, this seems to allow a really quick proof of the Basel problem. Letting x = 3, f(x)=x^2 -> f(3) = 9,

9=3+36/Pi^2*Sum[n=1->Infinity]­(-1)^(2n)/n^2 so after some basic algebra

6Pi^2/36=Pi^2/6=Sum[n=1->Infin­ity]1/n^2. I think Donny was sort of hinting at that, but I think that's interesting. Hopefully the next couple of videos will help establish convergence =)

[bluesrunthegame]

It's exciting for it's elegance not it's complexity.

[LiangRome]

Shut up and go fuck yourself. Some people are trying to learn.

[dannylee86]

okay,,,this one is quite clear and theoridically!!!!GOOD