Question

prove that $\lim_{n\rightarrow \infty} S_NF(\frac{1}{\pi n})=\int_{0}^{1}\frac{\sin(\frac{t}{\pi})}{2t}dt$

score 47 · Answer 1 · 2026-03-27 13:48:27

47

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prove that $\lim_{n\rightarrow \infty} S_NF(\frac{1}{\pi n})=\int_{0}^{1}\frac{\sin(\frac{t}{\pi})}{2t}dt$

Published on 27 Mar 2026 - 13:48

score 27 · Answer 2 · 2020-02-21 21:42:49

27

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Integral of a fraction of series

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259

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33

Views

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score 257 · Answer 5 · 2020-02-25 04:41:13

257

Views

Asymptotic expansion of $f(x)=\sum _{n=1}^{\infty } \frac{\sin \left(\sqrt{n}x\right)}{n}$ at the origin

Published on 25 Feb 2020 - 4:41

score 2.1k · Answer 6 · 2020-02-25 04:55:26

2.1k

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score 20 · Answer 7 · 2026-03-25 12:28:10

20

Views

Convergence of an infinite series $\sum_{n\geq 2}v_nw_n n^3$

Published on 25 Mar 2026 - 12:28

score 76 · Answer 8 · 2020-02-25 14:04:50

Find a function such that $ \int_{-\pi}^{\pi} f(x)\sin(nx)dx = \frac{(-1)^n}{\sqrt n} $ and $ \int_{-\pi}^{\pi} f(x)\cos(nx)dx = 0 $

score 194 · Answer 9 · 2020-02-25 15:02:20

194

Views

Calculate $\sum \limits_{n = 1}^{\infty} \frac{\cos 2n}{n^2}$

Published on 25 Feb 2020 - 15:02

score 351 · Answer 10 · 2020-02-26 08:47:17

351

Views

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score 55 · Answer 11 · 2026-03-27 04:38:47

55

Views

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score 17 · Answer 12 · 2026-03-16 00:34:53

17

Views

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score 916 · Answer 13 · 2020-02-28 14:50:31

916

Views

Why is the Fourier series of a continuously differentiable function absolutely convergent?

Published on 28 Feb 2020 - 14:50

score 60 · Answer 14 · 2020-02-28 15:41:52

60

Views

Use Parseval's Theorem to derive value of sum - Spot the error!

Published on 28 Feb 2020 - 15:41

score 40 · Answer 15 · 2020-02-28 22:56:09

40

Views

How to see that $l^{1}(\mathbb{Z}) \to C(S^1, \mathbb{C}): a \mapsto \sum_{n \in \mathbb{Z}}a_n z^n$ is not surjective?

Published on 28 Feb 2020 - 22:56

List Question

prove that $\lim_{n\rightarrow \infty} S_NF(\frac{1}{\pi n})=\int_{0}^{1}\frac{\sin(\frac{t}{\pi})}{2t}dt$

Integral of a fraction of series

Taylor series expansion approximation

How to sample continuous signal correctly?

Asymptotic expansion of $f(x)=\sum _{n=1}^{\infty } \frac{\sin \left(\sqrt{n}x\right)}{n}$ at the origin

Phase Shift in Fourier Series

Convergence of an infinite series $\sum_{n\geq 2}v_nw_n n^3$

Find a function such that $ \int_{-\pi}^{\pi} f(x)\sin(nx)dx = \frac{(-1)^n}{\sqrt n} $ and $ \int_{-\pi}^{\pi} f(x)\cos(nx)dx = 0 $

Calculate $\sum \limits_{n = 1}^{\infty} \frac{\cos 2n}{n^2}$

Fourier series on symmetric vs non-symmetric intervals

Fourier coefficients of a function

Non-negativity of the Toeplitz forms for harmonic functions

Why is the Fourier series of a continuously differentiable function absolutely convergent?

Use Parseval's Theorem to derive value of sum - Spot the error!

How to see that $l^{1}(\mathbb{Z}) \to C(S^1, \mathbb{C}): a \mapsto \sum_{n \in \mathbb{Z}}a_n z^n$ is not surjective?

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