Question

Fourier Series of $\sin^k(x/2)$

score 216 · Answer 1 · 2026-04-14 16:22:53

216

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Fourier Series of $\sin^k(x/2)$

Published on 14 Apr 2026 - 16:22

score 200 · Answer 2 · 2026-04-15 03:01:45

200

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Does the Series $\sum_{\substack{k=-\infty\\k\neq0}}^{\infty}\frac{e^{\frac{-\pi ik}{5}} - 1}{k}$ Converge?

Published on 15 Apr 2026 - 3:01

score 2.5k · Answer 3 · 2026-04-12 06:07:41

2.5k

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Series which are not Fourier Series

Published on 12 Apr 2026 - 6:07

score 1.2k · Answer 4 · 2026-04-11 04:35:35

1.2k

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Bounded Fourier Coefficients for monotonic functions

Published on 11 Apr 2026 - 4:35

score 293 · Answer 5 · 2026-04-12 00:41:57

293

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About $\sum_{k=1}^\infty \frac{b_k}{k}$, where $b_k$ are Fourier coefficients

Published on 12 Apr 2026 - 0:41

score 3.8k · Answer 6 · 2026-04-09 20:27:29

3.8k

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Differential equations, HEAT equation with insulated ends.

Published on 09 Apr 2026 - 20:27

score 2.9k · Answer 7 · 2026-04-10 08:40:19

2.9k

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heat equation solution

Published on 10 Apr 2026 - 8:40

score 111 · Answer 8 · 2026-04-12 23:56:33

111

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Recovering an Operator on $L^2$ Given its Action as a Composition on the Spectrum of $f$

Published on 12 Apr 2026 - 23:56

score 766 · Answer 9 · 2026-04-16 23:13:29

766

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Please check my answer to $\sum\limits_{i=1}^n \frac{\sin{(ix)}}{i} < 2\sqrt{\pi}$

Published on 16 Apr 2026 - 23:13

score 581 · Answer 10 · 2026-04-14 07:30:45

581

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Solving $f''+f=\sin x$ with Fourier series

Published on 14 Apr 2026 - 7:30

score 658 · Answer 11 · 2026-04-16 14:48:02

Let $a_{n}\downarrow 0$ and if series $\sum a_{n}\sin nx$ is a Fourier series of function $f\in L^{1}$ then $\sum \frac{a_{n}}{n}<+\infty.$

score 400 · Answer 12 · 2026-04-15 09:40:00

400

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To show $\displaystyle\sum_{n=2}^{\infty}\frac{\cos nx}{\log n}$ is a Fourier series.

Published on 15 Apr 2026 - 9:40

score 243 · Answer 13 · 2026-04-16 16:33:22

243

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Sum the series: $ S = \frac{1}{2} \cdot \sin\alpha + \frac{1\cdot 3}{2 \cdot 4} \sin{2\alpha} + \cdots \ \text{ad inf}$

Published on 16 Apr 2026 - 16:33

score 4.6k · Answer 14 · 2026-04-11 23:46:18

4.6k

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Solution of Laplace's equation in an annulus with constant Dirichlet conditions?

Published on 11 Apr 2026 - 23:46

score 1k · Answer 15 · 2026-04-11 10:24:32

1k

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What function do I pick for $\sum_{n=1}^{\infty}(1/n^6)$?

Published on 11 Apr 2026 - 10:24

List Question

Fourier Series of $\sin^k(x/2)$

Does the Series $\sum_{\substack{k=-\infty\\k\neq0}}^{\infty}\frac{e^{\frac{-\pi ik}{5}} - 1}{k}$ Converge?

Series which are not Fourier Series

Bounded Fourier Coefficients for monotonic functions

About $\sum_{k=1}^\infty \frac{b_k}{k}$, where $b_k$ are Fourier coefficients

Differential equations, HEAT equation with insulated ends.

heat equation solution

Recovering an Operator on $L^2$ Given its Action as a Composition on the Spectrum of $f$

Please check my answer to $\sum\limits_{i=1}^n \frac{\sin{(ix)}}{i} < 2\sqrt{\pi}$

Solving $f''+f=\sin x$ with Fourier series

Let $a_{n}\downarrow 0$ and if series $\sum a_{n}\sin nx$ is a Fourier series of function $f\in L^{1}$ then $\sum \frac{a_{n}}{n}<+\infty.$

To show $\displaystyle\sum_{n=2}^{\infty}\frac{\cos nx}{\log n}$ is a Fourier series.

Sum the series: $ S = \frac{1}{2} \cdot \sin\alpha + \frac{1\cdot 3}{2 \cdot 4} \sin{2\alpha} + \cdots \ \text{ad inf}$

Solution of Laplace's equation in an annulus with constant Dirichlet conditions?

What function do I pick for $\sum_{n=1}^{\infty}(1/n^6)$?

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