Question

How to justify interchange of summation and integral with $f_n(x)=x^2 \cos(2nx)/n$ on $[0, \pi/2]\times \mathbb{N}$?

score 181 · Answer 1 · 2026-04-14 17:51:06

181

Views

How to justify interchange of summation and integral with $f_n(x)=x^2 \cos(2nx)/n$ on $[0, \pi/2]\times \mathbb{N}$?

Published on 14 Apr 2026 - 17:51

score 26 · Answer 2 · 2026-04-13 04:18:20

26

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Finding the Fourier coefficients of a periodic function that is nonlinearly related to another periodic function.

Published on 13 Apr 2026 - 4:18

score 67 · Answer 3 · 2026-04-13 23:29:20

67

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Fourier series convergence for Banach space valued functions

Published on 13 Apr 2026 - 23:29

score 113 · Answer 4 · 2026-04-12 23:04:03

113

Views

Differentiating an exponent of a series

Published on 12 Apr 2026 - 23:04

score 26 · Answer 5 · 2026-04-16 09:34:37

26

Views

How can I solve this PDE $h(\phi_{xx}+\phi_{yy})+h_{x}\phi_{x}+h_{y}\phi_{y}=0, h=5-e^{-x^4-y^2}$

Published on 16 Apr 2026 - 9:34

score 60 · Answer 6 · 2026-04-28 13:53:23

60

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Fourier - $\mathscr{F}(f_a) $ knowing that $\mathscr{F}(\mathscr{F}(f))(x) = 2\pi f(-x) $,

Published on 28 Apr 2026 - 13:53

score 155 · Answer 7 · 2026-04-12 20:18:56

155

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Fourier coefficients of $\mathrm{e}^{\mathrm{e}^{\mathrm{i}x}}$?

Published on 12 Apr 2026 - 20:18

score 114 · Answer 8 · 2026-04-11 18:15:09

114

Views

Fourier series expansion of $\delta(x-1)$

Published on 11 Apr 2026 - 18:15

score 161 · Answer 9 · 2026-04-11 07:37:12

161

Views

Fourier Series for $f(x)=x+\cos(x)$ for $x \in [-\pi,\pi]$

Published on 11 Apr 2026 - 7:37

score 134 · Answer 10 · 2026-04-13 16:55:15

134

Views

Basisness of $|\sin(nx)|$ in $L^2(0, \pi/2)$

Published on 13 Apr 2026 - 16:55

score 369 · Answer 11 · 2026-04-16 18:55:51

369

Views

Proving that $\lim_{s \to 0^-} \int_{0}^{\infty} \frac{\arcsin(\sin x)}{x} x^{s} \, dx = \int_{0}^{\infty} \frac{\arcsin(\sin x)}{x} \, dx $

Published on 16 Apr 2026 - 18:55

score 136 · Answer 12 · 2026-04-14 01:56:44

136

Views

Showing if the following function is odd or even

Published on 14 Apr 2026 - 1:56

score 191 · Answer 13 · 2026-04-09 18:08:43

191

Views

How to interpret the Fourier Transform $X(\omega )$ (Foundational Questions)

Published on 09 Apr 2026 - 18:08

score 57 · Answer 14 · 2026-04-12 02:02:01

57

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Why this transverse wave appear in this function?

Published on 12 Apr 2026 - 2:02

score 58 · Answer 15 · 2026-04-10 16:11:55

58

Views

Question about summation of a specific Fourier series

Published on 10 Apr 2026 - 16:11

List Question

How to justify interchange of summation and integral with $f_n(x)=x^2 \cos(2nx)/n$ on $[0, \pi/2]\times \mathbb{N}$?

Finding the Fourier coefficients of a periodic function that is nonlinearly related to another periodic function.

Fourier series convergence for Banach space valued functions

Differentiating an exponent of a series

How can I solve this PDE $h(\phi_{xx}+\phi_{yy})+h_{x}\phi_{x}+h_{y}\phi_{y}=0, h=5-e^{-x^4-y^2}$

Fourier - $\mathscr{F}(f_a) $ knowing that $\mathscr{F}(\mathscr{F}(f))(x) = 2\pi f(-x) $,

Fourier coefficients of $\mathrm{e}^{\mathrm{e}^{\mathrm{i}x}}$?

Fourier series expansion of $\delta(x-1)$

Fourier Series for $f(x)=x+\cos(x)$ for $x \in [-\pi,\pi]$

Basisness of $|\sin(nx)|$ in $L^2(0, \pi/2)$

Proving that $\lim_{s \to 0^-} \int_{0}^{\infty} \frac{\arcsin(\sin x)}{x} x^{s} \, dx = \int_{0}^{\infty} \frac{\arcsin(\sin x)}{x} \, dx $

Showing if the following function is odd or even

How to interpret the Fourier Transform $X(\omega )$ (Foundational Questions)

Why this transverse wave appear in this function?

Question about summation of a specific Fourier series

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