List questions from fourier-series

Published on 01 Dec 2016 - 2:08

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Closed form of the Dirichlet kernel: $\sum\limits_{n=-N}^{N} e^{inx} =\frac{\sin((N+1/2)x}{\sin(x/2)}$

Published on 01 Dec 2016 - 9:06

161

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Variants of Parseval's relation

Published on 01 Dec 2016 - 15:04

66

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$\Vert . \Vert_{H^1}$ is induced by an inner product and $(H_0^1, \Vert . \Vert_{H^1})$ is a Hilbert space

Published on 02 Dec 2016 - 14:07

63

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Derive a Fourier expansion of the piece-wise function and prove $\pi = \sqrt{\sum_{n=1}^\infty (\frac{6}{n^2})} $

Published on 03 Dec 2016 - 16:59

383

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Stuck in the proof that if $f\in L^1(\mathbb{T})$ and $\hat{f}\in\ell^1(\mathbb{Z})$, then $f\in L^2(\mathbb{T})$

Published on 04 Dec 2016 - 18:57

212

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Analytically solving an infinite series of periodic functions

Published on 27 Mar 2026 - 2:59

315

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Showing $\sum_{n=1}^\infty\frac{1-(-1)^n}{n^2} = \frac{\pi^2}{4}$ from Fourier expansion

Published on 06 Dec 2016 - 12:32

592

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fourier, sobolev and equivalent norms.

Published on 07 Dec 2016 - 0:25

534

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Finding particular solution to 1D - wave equation given general solution.

Published on 07 Dec 2016 - 15:05

55

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sobolev and norms

Published on 08 Dec 2016 - 21:41

56

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Lipschitz constant of Fejer kernel is O(n)

Published on 09 Dec 2016 - 6:16

375

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Fourier sine series over $[0,\pi]$ vs over $[-\pi,\pi]$?

Published on 10 Dec 2016 - 21:15

414

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Magnitude of discontinuity

Published on 10 Dec 2016 - 21:42

232

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Why is L'Hopital's rule failing for this Fourier Coefficient?

Published on 11 Dec 2016 - 4:33

List Question

fourier coefficients and characteristic

Closed form of the Dirichlet kernel: $\sum\limits_{n=-N}^{N} e^{inx} =\frac{\sin((N+1/2)x}{\sin(x/2)}$

Variants of Parseval's relation

$\Vert . \Vert_{H^1}$ is induced by an inner product and $(H_0^1, \Vert . \Vert_{H^1})$ is a Hilbert space

Derive a Fourier expansion of the piece-wise function and prove $\pi = \sqrt{\sum_{n=1}^\infty (\frac{6}{n^2})} $

Stuck in the proof that if $f\in L^1(\mathbb{T})$ and $\hat{f}\in\ell^1(\mathbb{Z})$, then $f\in L^2(\mathbb{T})$

Analytically solving an infinite series of periodic functions

Showing $\sum_{n=1}^\infty\frac{1-(-1)^n}{n^2} = \frac{\pi^2}{4}$ from Fourier expansion

fourier, sobolev and equivalent norms.

Finding particular solution to 1D - wave equation given general solution.

sobolev and norms

Lipschitz constant of Fejer kernel is O(n)

Fourier sine series over $[0,\pi]$ vs over $[-\pi,\pi]$?

Magnitude of discontinuity

Why is L'Hopital's rule failing for this Fourier Coefficient?

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