Question

How to calculate Fourier series via Cauchy Product?

score 109 · Answer 1 · 2026-04-09 11:41:40

109

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How to calculate Fourier series via Cauchy Product?

Published on 09 Apr 2026 - 11:41

score 165 · Answer 2 · 2026-04-30 06:15:57

165

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How are Fourier Transform and Fourier Series used in practicality?

Published on 30 Apr 2026 - 6:15

score 149 · Answer 3 · 2026-04-15 06:27:52

149

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Prove $\cos(ax)=\frac{\sin(\pi a)}{\pi a}+\sum_{n=1}^{\infty }(-1)^{n}\frac{2a\sin(\pi a)}{\pi (a^{2}-n^{2})}\cos(nx)$

Published on 15 Apr 2026 - 6:27

score 165 · Answer 4 · 2026-04-16 16:48:14

165

Views

If $f(x)$ is Henstock-Kurzweil integrable on $[a,b]$, then is $f(x)\mathrm{e}^{\mathrm{i}x}$ also Henstock-Kurzweil integrable on $[a,b]$?

Published on 16 Apr 2026 - 16:48

score 272 · Answer 5 · 2026-04-16 01:26:18

272

Views

Using Fourier series to compute $1-\frac1{3^2}-\frac1{5^2}+\frac1{7^2}+\cdots$

Published on 16 Apr 2026 - 1:26

score 88 · Answer 6 · 2026-04-11 15:16:26

88

Views

How to solve the Diffusion PDE with Fourier Series

Published on 11 Apr 2026 - 15:16

score 794 · Answer 7 · 2026-04-30 06:16:10

794

Views

Fourier Transform of Odd Functions

Published on 30 Apr 2026 - 6:16

score 33 · Answer 8 · 2026-04-14 23:03:17

33

Views

Determine the convergence of Fourier series and find the function to which it converges

Published on 14 Apr 2026 - 23:03

score 157 · Answer 9 · 2026-04-16 03:32:43

157

Views

Prove $f(x)=\frac{1}{\pi}+\frac{1}{2}\sin(2x)-\frac{2}{\pi}\displaystyle\sum_{n=1}^{\infty}\frac{\cos(4nx)}{(2n-1)(2n+1)}$ Fourier Series

Published on 16 Apr 2026 - 3:32

score 61 · Answer 10 · 2026-04-30 07:20:59

61

Views

Representation of $\sum_{k=1}^{\infty} \frac{f^{(k)}(a)}{k!} k^{-p} $ in terms of another series

Published on 30 Apr 2026 - 7:20

score 189 · Answer 11 · 2026-04-15 04:11:26

189

Views

An easy version of Riemann-Lebesgue Lemma on $L^2([-\pi,\pi])$

Published on 15 Apr 2026 - 4:11

score 27 · Answer 12 · 2026-04-18 18:04:38

27

Views

Determine where function is discontinuous by its fourier coefficients

Published on 18 Apr 2026 - 18:04

score 140 · Answer 13 · 2026-04-11 22:25:52

140

Views

Evaluating a limit of a Fourier series

Published on 11 Apr 2026 - 22:25

score 68 · Answer 14 · 2026-04-09 12:12:00

68

Views

Closed formula for variation of Fourier series of Bernoulli polynomials

Published on 09 Apr 2026 - 12:12

score 96 · Answer 15 · 2026-04-14 22:46:08

96

Views

Finding Fourier coefficients $a_n$ of $\ln|\sin(\frac{x}{2})|$

Published on 14 Apr 2026 - 22:46

List Question

How to calculate Fourier series via Cauchy Product?

How are Fourier Transform and Fourier Series used in practicality?

Prove $\cos(ax)=\frac{\sin(\pi a)}{\pi a}+\sum_{n=1}^{\infty }(-1)^{n}\frac{2a\sin(\pi a)}{\pi (a^{2}-n^{2})}\cos(nx)$

If $f(x)$ is Henstock-Kurzweil integrable on $[a,b]$, then is $f(x)\mathrm{e}^{\mathrm{i}x}$ also Henstock-Kurzweil integrable on $[a,b]$?

Using Fourier series to compute $1-\frac1{3^2}-\frac1{5^2}+\frac1{7^2}+\cdots$

How to solve the Diffusion PDE with Fourier Series

Fourier Transform of Odd Functions

Determine the convergence of Fourier series and find the function to which it converges

Prove $f(x)=\frac{1}{\pi}+\frac{1}{2}\sin(2x)-\frac{2}{\pi}\displaystyle\sum_{n=1}^{\infty}\frac{\cos(4nx)}{(2n-1)(2n+1)}$ Fourier Series

Representation of $\sum_{k=1}^{\infty} \frac{f^{(k)}(a)}{k!} k^{-p} $ in terms of another series

An easy version of Riemann-Lebesgue Lemma on $L^2([-\pi,\pi])$

Determine where function is discontinuous by its fourier coefficients

Evaluating a limit of a Fourier series

Closed formula for variation of Fourier series of Bernoulli polynomials

Finding Fourier coefficients $a_n$ of $\ln|\sin(\frac{x}{2})|$

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