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Question on Fourier Series Equivalency

score 38 · Answer 1 · 2023-02-10 21:05:27

38

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Question on Fourier Series Equivalency

Published on 10 Feb 2023 - 21:05

score 50 · Answer 2 · 2026-02-23 04:44:36

50

Views

Finding a closed expression for the Riemann zeta function at even inputs

Published on 23 Feb 2026 - 4:44

score 84 · Answer 3 · 2026-02-23 04:46:32

84

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Calculate the sum of $\lim_{N\rightarrow \infty} \sum_{-N}^N 1/(n+e)$

Published on 23 Feb 2026 - 4:46

score 96 · Answer 4 · 2026-03-31 07:52:59

96

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The solution of a set of equations is about to appear but still elusive.

Published on 31 Mar 2026 - 7:52

score 63 · Answer 5 · 2026-04-07 00:41:04

63

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Why for periodic function the fourier expansion is a series (sum over $\mathbb{Z}$) and for non-periodic functions an integral (sum over$\mathbb{R}$)?

Published on 07 Apr 2026 - 0:41

score 68 · Answer 6 · 2026-04-03 07:31:21

68

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If the Fourier coefficients of $f$ are $\hat{f} \in \ell_{2}$ then $f \in L_2$?

Published on 03 Apr 2026 - 7:31

score 466 · Answer 7 · 2023-02-19 16:50:56

466

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Fourier series of $\cos (x) $ in $[-\pi , \pi ] $ , coefficients are giving $0$

Published on 19 Feb 2023 - 16:50

score 174 · Answer 8 · 2026-04-01 08:06:12

174

Views

Proving that $\sum_{n=1}^{\infty} \frac{\sin(nx)}{n^\alpha}$ is not the Fourier Series of a Riemann Integrable function

Published on 01 Apr 2026 - 8:06

score 476 · Answer 9 · 2026-03-26 08:23:02

476

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Evaluate $\int_{0}^{\pi/2} \ln\left[ \tan\left ( \frac{\theta}{2}\right) \right ]^2 K\left ( \sin\theta \right )\text{d}\theta$

Published on 26 Mar 2026 - 8:23

score 67 · Answer 10 · 2023-03-02 06:11:40

67

Views

A question on the Riemann-Lebesgue Leamma

Published on 02 Mar 2023 - 6:11

score 96 · Answer 11 · 2026-04-01 16:20:19

96

Views

maximum Fourier coefficient among all bounded real continuous periodic functions

Published on 01 Apr 2026 - 16:20

score 46 · Answer 12 · 2026-04-03 03:17:27

46

Views

Find the sum $ \sum_{-\infty}^{\infty} \frac{1}{1 + (x + n)^2} $

Published on 03 Apr 2026 - 3:17

score 73 · Answer 13 · 2023-03-06 19:54:13

73

Views

Proving a property of the Fourier coefficients of a continuous function

Published on 06 Mar 2023 - 19:54

score 227 · Answer 14 · 2026-04-03 07:31:21

227

Views

If the Fourier coefficient $\hat{f}(k)$ of $f\in C^1(\mathbb T)$ is zero for all $|k|<N$, then $\|f\|_{L^\infty}\leq \frac CN \|f'\|_{L^\infty}$

Published on 03 Apr 2026 - 7:31

score 73 · Answer 15 · 2023-03-07 18:12:59

73

Views

Dirichlet kernel in product form

Published on 07 Mar 2023 - 18:12

List Question

Question on Fourier Series Equivalency

Finding a closed expression for the Riemann zeta function at even inputs

Calculate the sum of $\lim_{N\rightarrow \infty} \sum_{-N}^N 1/(n+e)$

The solution of a set of equations is about to appear but still elusive.

Why for periodic function the fourier expansion is a series (sum over $\mathbb{Z}$) and for non-periodic functions an integral (sum over$\mathbb{R}$)?

If the Fourier coefficients of $f$ are $\hat{f} \in \ell_{2}$ then $f \in L_2$?

Fourier series of $\cos (x) $ in $[-\pi , \pi ] $ , coefficients are giving $0$

Proving that $\sum_{n=1}^{\infty} \frac{\sin(nx)}{n^\alpha}$ is not the Fourier Series of a Riemann Integrable function

Evaluate $\int_{0}^{\pi/2} \ln\left[ \tan\left ( \frac{\theta}{2}\right) \right ]^2 K\left ( \sin\theta \right )\text{d}\theta$

A question on the Riemann-Lebesgue Leamma

maximum Fourier coefficient among all bounded real continuous periodic functions

Find the sum $ \sum_{-\infty}^{\infty} \frac{1}{1 + (x + n)^2} $

Proving a property of the Fourier coefficients of a continuous function

If the Fourier coefficient $\hat{f}(k)$ of $f\in C^1(\mathbb T)$ is zero for all $|k|<N$, then $\|f\|_{L^\infty}\leq \frac CN \|f'\|_{L^\infty}$

Dirichlet kernel in product form

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