Question

reciprocal of a Fourier Cosine series

score 183 · Answer 1 · 2026-04-14 10:09:31

183

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reciprocal of a Fourier Cosine series

Published on 14 Apr 2026 - 10:09

score 1.5k · Answer 2 · 2026-04-12 14:25:40

1.5k

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Find the Fourier series for the function defined by:

Published on 12 Apr 2026 - 14:25

score 103 · Answer 3 · 2026-04-12 23:38:20

103

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Proof verification : regarding pointwise and norm convergence of a fourier sequence of $L^2$ function

Published on 12 Apr 2026 - 23:38

score 84 · Answer 4 · 2026-04-17 15:25:58

Use the sine Fourier series for $x$ and $x^2$ to show $1-\frac{1}{3^3} + \frac{1}{5^3} - \frac{1}{7^3} + ... = \frac{\pi ^3}{32}$

score 68 · Answer 5 · 2026-04-17 08:47:56

Let $1 + \frac{1}{3^3} + \frac{1}{5^3} + \frac{1}{7^3} + \dots=s$, show that then $\sum_1^\infty\frac{1}{n^3}=\frac{8}{7}s$

score 817 · Answer 6 · 2026-04-08 22:39:49

817

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Confusion regarding Gibbs phenomenon

Published on 08 Apr 2026 - 22:39

score 31 · Answer 7 · 2026-04-16 10:49:19

31

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Find the cosine series for the function defined by $f(x)=2$, $0 \le x \lt 1$ and $f(x)=0$, $1 \le x \lt 2$.

Published on 16 Apr 2026 - 10:49

score 171 · Answer 8 · 2026-04-08 09:16:58

171

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Possible to expand a constant function as a series of sines without phase?

Published on 08 Apr 2026 - 9:16

score 84 · Answer 9 · 2026-04-13 06:56:44

How does one find the Fourier Series for a non-periodic function on an arbitrary interval $[-\frac{L}{2},\frac{L}{2}]$ using the complex exponential?

score 147 · Answer 10 · 2026-04-13 16:58:14

147

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Find the Fourier series for $e^{-|x|}$ over $[-\pi,\pi]$

Published on 13 Apr 2026 - 16:58

score 103 · Answer 11 · 2026-04-11 12:03:57

103

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Is $\sum_{k=1}^\infty \dfrac{1}{k^2}+\dfrac{1}{(k+1)^2}=\sum_{k=1}^\infty \dfrac{1}{k^2}$?

Published on 11 Apr 2026 - 12:03

score 93 · Answer 12 · 2026-04-17 07:48:11

93

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Proving the convergence/divergence of $\sum_{n=1}^\infty \frac{\cos\ n}{n} (1+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{n}})$

Published on 17 Apr 2026 - 7:48

score 51 · Answer 13 · 2026-03-28 22:55:04

51

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How does $\cos(x)\cdot\cos\left(\frac{3}{2}x\right)$ become $\frac{1}{2}\left(\cos\left(\frac{1}{2}x\right) + \cos\left(\frac{5}{2}x\right)\right)$?

Published on 28 Mar 2026 - 22:55

score 2.1k · Answer 14 · 2026-04-17 03:39:45

2.1k

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Convergent Fourier series of continuous function

Published on 17 Apr 2026 - 3:39

score 488 · Answer 15 · 2026-04-13 00:29:23

488

Views

Uniform convergence fourier series |sin(x)|

Published on 13 Apr 2026 - 0:29

List Question

reciprocal of a Fourier Cosine series

Find the Fourier series for the function defined by:

Proof verification : regarding pointwise and norm convergence of a fourier sequence of $L^2$ function

Use the sine Fourier series for $x$ and $x^2$ to show $1-\frac{1}{3^3} + \frac{1}{5^3} - \frac{1}{7^3} + ... = \frac{\pi ^3}{32}$

Let $1 + \frac{1}{3^3} + \frac{1}{5^3} + \frac{1}{7^3} + \dots=s$, show that then $\sum_1^\infty\frac{1}{n^3}=\frac{8}{7}s$

Confusion regarding Gibbs phenomenon

Find the cosine series for the function defined by $f(x)=2$, $0 \le x \lt 1$ and $f(x)=0$, $1 \le x \lt 2$.

Possible to expand a constant function as a series of sines without phase?

How does one find the Fourier Series for a non-periodic function on an arbitrary interval $[-\frac{L}{2},\frac{L}{2}]$ using the complex exponential?

Find the Fourier series for $e^{-|x|}$ over $[-\pi,\pi]$

Is $\sum_{k=1}^\infty \dfrac{1}{k^2}+\dfrac{1}{(k+1)^2}=\sum_{k=1}^\infty \dfrac{1}{k^2}$?

Proving the convergence/divergence of $\sum_{n=1}^\infty \frac{\cos\ n}{n} (1+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{n}})$

How does $\cos(x)\cdot\cos\left(\frac{3}{2}x\right)$ become $\frac{1}{2}\left(\cos\left(\frac{1}{2}x\right) + \cos\left(\frac{5}{2}x\right)\right)$?

Convergent Fourier series of continuous function

Uniform convergence fourier series |sin(x)|

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