Question

Fourier series of $f(x) = \cos(x)$

score 90 · Answer 1 · 2026-04-15 09:29:35

90

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Fourier series of $f(x) = \cos(x)$

Published on 15 Apr 2026 - 9:29

score 69 · Answer 2 · 2026-05-15 04:10:43

69

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Fourier series expansion of a $L^2$ function.

Published on 15 May 2026 - 4:10

score 50 · Answer 3 · 2026-04-16 14:22:16

50

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Proof that $\sum_{k = 0}^{N-1} \cos \left(\frac{2 \pi}{N} \left( k + \frac{1}{2} \right) \right) = 0$

Published on 16 Apr 2026 - 14:22

score 79 · Answer 4 · 2026-04-09 15:21:38

79

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Poisson Summation at Half Integers

Published on 09 Apr 2026 - 15:21

score 35 · Answer 5 · 2026-04-30 10:57:54

35

Views

Finding solutions to $ \sin\left(n \pi \frac{T_p}{T}\right) - \sin\left(n \pi \frac{T_0}{T}\right) = \sin\left( \frac{{n \pi}}{2}\right) $

Published on 30 Apr 2026 - 10:57

score 65 · Answer 6 · 2026-04-16 04:16:02

65

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Show that $\underset{N\to\infty}{\lim}\int_{-\pi}^\pi [g(t)\cos(\frac{t}{2})]\sin(Nt)dt=0$, where $g(t)=\frac{f(x-t)-f(x)}{\sin(t/2)}$.

Published on 16 Apr 2026 - 4:16

score 169 · Answer 7 · 2026-04-11 20:44:43

169

Views

Frequency peak always appearing at half of Nyquist frequency in Fourier transform

Published on 11 Apr 2026 - 20:44

score 152 · Answer 8 · 2026-05-05 14:46:46

152

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Expressing $ \sum_{n=1}^{\infty}\frac{\mu(n)}{n^{2}} \left \lfloor x^{1/n}-1 \right \rfloor$ in terms of the nontrivial zeros of $\zeta(s)$

Published on 05 May 2026 - 14:46

score 41 · Answer 9 · 2026-04-14 06:50:58

41

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What is the value of the sum of $e^{i(-ak^2 + bk)}$ when $k$ goes through every integer?

Published on 14 Apr 2026 - 6:50

score 43 · Answer 10 · 2026-04-10 16:48:37

43

Views

Upper bound for sum of waves

Published on 10 Apr 2026 - 16:48

score 130 · Answer 11 · 2026-04-13 22:09:20

130

Views

About the Dirichlet conditions and the Fourier series of the sine function

Published on 13 Apr 2026 - 22:09

score 98 · Answer 12 · 2026-04-12 02:00:01

98

Views

Is there a hyperbolic variant of the sine-cosine fourier series?

Published on 12 Apr 2026 - 2:00

score 160 · Answer 13 · 2026-04-11 13:15:24

160

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Infinite series Sum of zeroth order Bessel Functions of first kind

Published on 11 Apr 2026 - 13:15

score 41 · Answer 14 · 2026-04-11 18:50:31

41

Views

Doing transformations on trignometric functions

Published on 11 Apr 2026 - 18:50

score 40 · Answer 15 · 2026-05-14 16:53:44

40

Views

The norm and the Fourier coefficient if the inner product $\langle f(x), f(x)\rangle$ is negative.

Published on 14 May 2026 - 16:53

List Question

Fourier series of $f(x) = \cos(x)$

Fourier series expansion of a $L^2$ function.

Proof that $\sum_{k = 0}^{N-1} \cos \left(\frac{2 \pi}{N} \left( k + \frac{1}{2} \right) \right) = 0$

Poisson Summation at Half Integers

Finding solutions to $ \sin\left(n \pi \frac{T_p}{T}\right) - \sin\left(n \pi \frac{T_0}{T}\right) = \sin\left( \frac{{n \pi}}{2}\right) $

Show that $\underset{N\to\infty}{\lim}\int_{-\pi}^\pi [g(t)\cos(\frac{t}{2})]\sin(Nt)dt=0$, where $g(t)=\frac{f(x-t)-f(x)}{\sin(t/2)}$.

Frequency peak always appearing at half of Nyquist frequency in Fourier transform

Expressing $ \sum_{n=1}^{\infty}\frac{\mu(n)}{n^{2}} \left \lfloor x^{1/n}-1 \right \rfloor$ in terms of the nontrivial zeros of $\zeta(s)$

What is the value of the sum of $e^{i(-ak^2 + bk)}$ when $k$ goes through every integer?

Upper bound for sum of waves

About the Dirichlet conditions and the Fourier series of the sine function

Is there a hyperbolic variant of the sine-cosine fourier series?

Infinite series Sum of zeroth order Bessel Functions of first kind

Doing transformations on trignometric functions

The norm and the Fourier coefficient if the inner product $\langle f(x), f(x)\rangle$ is negative.

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