Question

Computation of $\int_0^{2\pi} \frac{x^2 \sin{x}}{1 - 2a\cos{x} + a^2}$

score 448 · Answer 1 · 2026-04-15 18:10:10

448

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Computation of $\int_0^{2\pi} \frac{x^2 \sin{x}}{1 - 2a\cos{x} + a^2}$

Published on 15 Apr 2026 - 18:10

score 67 · Answer 2 · 2026-04-17 01:10:36

67

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Calculate $\int\limits_0^{\pi} \frac{\cos(mx)}{1 - a \cdot\cos x}\,dx, m \in \mathbb{N}, |a| < 1$ using Fourier series

Published on 17 Apr 2026 - 1:10

score 83 · Answer 3 · 2026-04-09 04:49:40

83

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Fourier series of a fraction involving trigonometric functions

Published on 09 Apr 2026 - 4:49

score 32 · Answer 4 · 2026-04-17 03:18:23

32

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If $f(x)$ has period $2\pi$, then $F(t) = f(\omega t) = f(\frac{2\pi}{T}t)$ has period T

Published on 17 Apr 2026 - 3:18

score 93 · Answer 5 · 2026-04-16 12:33:18

93

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decompose to Fourier and calculate integral $\int \limits_{0}^{2\pi} \frac{x\cos{mx}}{1-a\cos{x}}dx$

Published on 16 Apr 2026 - 12:33

score 266 · Answer 6 · 2026-04-25 05:54:07

266

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Show that Fourier Series $\sum_{k=-\infty}^{\infty}\frac{-ie^{ikx}}{k}$ converges to original $f(x)$

Published on 25 Apr 2026 - 5:54

score 128 · Answer 7 · 2026-04-16 11:58:55

128

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Find the fourier series and the cesaro mean for

Published on 16 Apr 2026 - 11:58

score 201 · Answer 8 · 2026-04-15 16:42:09

201

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Fourier series for $\phi(x) = x$ on $[-l,l]$

Published on 15 Apr 2026 - 16:42

score 84 · Answer 9 · 2026-04-12 09:32:56

84

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Sum of two infinite series - Fourier Series

Published on 12 Apr 2026 - 9:32

score 108 · Answer 10 · 2026-04-14 19:29:47

108

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Integrate the Fourier series to find the sine series for $x^3 - l^2 x$

Published on 14 Apr 2026 - 19:29

score 2.2k · Answer 11 · 2026-04-15 03:23:28

2.2k

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Fourier series for $\operatorname{sgn}(\sin(x))+\operatorname{sgn}(\cos(x))$

Published on 15 Apr 2026 - 3:23

score 577 · Answer 12 · 2026-04-16 14:52:15

577

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Why does $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$ span $L^2([-L,L])?$

Published on 16 Apr 2026 - 14:52

score 233 · Answer 13 · 2026-04-12 01:39:26

233

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Does the Fourier series converge pointwise?

Published on 12 Apr 2026 - 1:39

score 702 · Answer 14 · 2026-04-14 22:53:34

702

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Convergence of Fourier inverse theorem and Fourier series

Published on 14 Apr 2026 - 22:53

score 198 · Answer 15 · 2026-04-14 03:59:06

198

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Using the Fourier transform to prove that $\int_0^\infty\frac{\sin u}{u}du$ is $\frac{\pi}{2}$

Published on 14 Apr 2026 - 3:59

List Question

Computation of $\int_0^{2\pi} \frac{x^2 \sin{x}}{1 - 2a\cos{x} + a^2}$

Calculate $\int\limits_0^{\pi} \frac{\cos(mx)}{1 - a \cdot\cos x}\,dx, m \in \mathbb{N}, |a| < 1$ using Fourier series

Fourier series of a fraction involving trigonometric functions

If $f(x)$ has period $2\pi$, then $F(t) = f(\omega t) = f(\frac{2\pi}{T}t)$ has period T

decompose to Fourier and calculate integral $\int \limits_{0}^{2\pi} \frac{x\cos{mx}}{1-a\cos{x}}dx$

Show that Fourier Series $\sum_{k=-\infty}^{\infty}\frac{-ie^{ikx}}{k}$ converges to original $f(x)$

Find the fourier series and the cesaro mean for

Fourier series for $\phi(x) = x$ on $[-l,l]$

Sum of two infinite series - Fourier Series

Integrate the Fourier series to find the sine series for $x^3 - l^2 x$

Fourier series for $\operatorname{sgn}(\sin(x))+\operatorname{sgn}(\cos(x))$

Why does $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$ span $L^2([-L,L])?$

Does the Fourier series converge pointwise?

Convergence of Fourier inverse theorem and Fourier series

Using the Fourier transform to prove that $\int_0^\infty\frac{\sin u}{u}du$ is $\frac{\pi}{2}$

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