Question

Showing that the functions $\sin(2n+1)x$ are orthogonal with respect to the inner product $\int_0^{\pi/2}f(x)g(x)dx$

score 1.2k · Answer 1 · 2026-03-25 13:49:31

Showing that the functions $\sin(2n+1)x$ are orthogonal with respect to the inner product $\int_0^{\pi/2}f(x)g(x)dx$

Published on 25 Mar 2026 - 13:49

score 297 · Answer 2 · 2018-04-24 06:32:39

If f $\in$ $L^{1}[\pi]$ such that fourier coefficients of $f$ are absolutely summable. Then partial fourier sums of $f$ converge to $f$?

score 686 · Answer 3 · 2018-04-24 14:20:03

686

Views

Fourier series of $ \arctan( \frac{2a \sin(x) }{ 1-a^2} ) $

Published on 24 Apr 2018 - 14:20

score 237 · Answer 4 · 2026-03-25 22:04:07

237

Views

Calculate Fourier coefficients of a product

Published on 25 Mar 2026 - 22:04

score 55 · Answer 5 · 2026-03-23 10:21:25

55

Views

Proving some identities using Fourier series

Published on 23 Mar 2026 - 10:21

score 170 · Answer 6 · 2018-04-25 18:37:09

170

Views

Determine whether Certain Series is Fourier Series of Some Integrable Function

Published on 25 Apr 2018 - 18:37

score 93 · Answer 7 · 2018-04-25 18:56:46

Given any countable subset $A$ of $[-\pi, \pi]$, there exists a function $f \in C[-\pi, \pi]$ whose Fourier series diverges for all $x$ $\in$ $A$.

score 1.5k · Answer 8 · 2018-04-25 20:09:13

1.5k

Views

How to understand conjugate in orthogonal system of functions

Published on 25 Apr 2018 - 20:09

score 70 · Answer 9 · 2018-04-27 02:02:58

70

Views

Quantitative control over Caratheodory Extension of a Riemann map, for the theorem of Bohr-Pal

Published on 27 Apr 2018 - 2:02

score 43 · Answer 10 · 2018-04-28 22:02:13

43

Views

Doubt regarding complex Fourier series coefficients

Published on 28 Apr 2018 - 22:02

score 41 · Answer 11 · 2026-03-24 22:07:41

41

Views

Compute the coefficients of $\sum\limits_{n=1}^\infty A_n\sin\frac{n\pi x}{l}=\frac{x^2-x}{4}$

Published on 24 Mar 2026 - 22:07

score 137 · Answer 12 · 2018-04-29 08:27:52

137

Views

Computing Fourier Series and it's modes of convergence.

Published on 29 Apr 2018 - 8:27

score 143 · Answer 13 · 2018-04-29 22:26:30

143

Views

Prove that every sufficiently large Fourier coefficient is positive

Published on 29 Apr 2018 - 22:26

score 337 · Answer 14 · 2018-04-29 23:13:36

337

Views

Whats is the sum of series for each $0\le x\le 3$?

Published on 29 Apr 2018 - 23:13

score 336 · Answer 15 · 2018-04-30 02:03:10

336

Views

Injectivity of fourier coefficient map

Published on 30 Apr 2018 - 2:03

List Question

Showing that the functions $\sin(2n+1)x$ are orthogonal with respect to the inner product $\int_0^{\pi/2}f(x)g(x)dx$

If f $\in$ $L^{1}[\pi]$ such that fourier coefficients of $f$ are absolutely summable. Then partial fourier sums of $f$ converge to $f$?

Fourier series of $ \arctan( \frac{2a \sin(x) }{ 1-a^2} ) $

Calculate Fourier coefficients of a product

Proving some identities using Fourier series

Determine whether Certain Series is Fourier Series of Some Integrable Function

Given any countable subset $A$ of $[-\pi, \pi]$, there exists a function $f \in C[-\pi, \pi]$ whose Fourier series diverges for all $x$ $\in$ $A$.

How to understand conjugate in orthogonal system of functions

Quantitative control over Caratheodory Extension of a Riemann map, for the theorem of Bohr-Pal

Doubt regarding complex Fourier series coefficients

Compute the coefficients of $\sum\limits_{n=1}^\infty A_n\sin\frac{n\pi x}{l}=\frac{x^2-x}{4}$

Computing Fourier Series and it's modes of convergence.

Prove that every sufficiently large Fourier coefficient is positive

Whats is the sum of series for each $0\le x\le 3$?

Injectivity of fourier coefficient map

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