Question

Evaluate $s(x)$ for $0<x<1$. $ s(x)=\sum_{j=1}^{\infty} \frac{x^j+(1-x)^j}{j^2} . $

score 41 · Answer 1 · 2026-05-14 16:14:41

41

Views

Evaluate $s(x)$ for $0<x<1$. $ s(x)=\sum_{j=1}^{\infty} \frac{x^j+(1-x)^j}{j^2} . $

Published on 14 May 2026 - 16:14

score 28 · Answer 2 · 2026-04-14 02:34:12

28

Views

Finding $c_0$ in Complex form of Fourier Series of $x^2$ where $0\le x\le 2\pi$

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score 132 · Answer 3 · 2026-04-09 11:58:35

132

Views

Abbott's derivation of Fejer's kernel

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score 426 · Answer 4 · 2026-04-12 03:09:04

426

Views

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score 163 · Answer 5 · 2026-04-13 21:41:52

163

Views

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score 30 · Answer 6 · 2026-04-16 03:27:03

30

Views

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score 124 · Answer 7 · 2026-04-11 08:52:42

124

Views

Can the usual Fourier series of a function be viewed as that defined with respect to an orthonormal system of functions?

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score 163 · Answer 8 · 2026-04-11 16:51:56

163

Views

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score 38 · Answer 9 · 2026-04-11 16:24:33

38

Views

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score 53 · Answer 10 · 2026-04-10 21:54:14

53

Views

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score 90 · Answer 11 · 2026-04-12 02:36:46

90

Views

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score 262 · Answer 12 · 2026-04-14 11:14:56

262

Views

Fourier series of $\{x\}$ (the fractional part of $x$ ) is weird: "$\{1\} = 0.5$"

Published on 14 Apr 2026 - 11:14

score 195 · Answer 13 · 2026-04-11 10:59:19

195

Views

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score 117 · Answer 14 · 2026-04-10 07:38:14

117

Views

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Published on 10 Apr 2026 - 7:38

score 118 · Answer 15 · 2026-04-12 08:28:06

118

Views

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List Question

Evaluate $s(x)$ for $0<x<1$. $ s(x)=\sum_{j=1}^{\infty} \frac{x^j+(1-x)^j}{j^2} . $

Finding $c_0$ in Complex form of Fourier Series of $x^2$ where $0\le x\le 2\pi$

Abbott's derivation of Fejer's kernel

A (simple) misunderstanding of quarter-wave symmetry "proof" in Fourier series

What are the range of Fourier coefficients such that the resultant function is positive and bounded?

Problem with exponential form of Fourier Series of $x^2$ while writing the $c_0$ separately

Can the usual Fourier series of a function be viewed as that defined with respect to an orthonormal system of functions?

Piecewise constant solution of waves

Frequency multiplier.

Fourier series and partial fraction expansion of πcsc(πz)/z

How to rewrite trigonometric functions for Fourier Series

Fourier series of $\{x\}$ (the fractional part of $x$ ) is weird: "$\{1\} = 0.5$"

Fourier Series Relation between "Conjugate" functions

How to convert this integral to a contour integral over the unit circle?

1d Heat equation with variable Area

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