Question

Finding the infinite sum of a Fourier Series at a given $x$

score 247 · Answer 1 · 2026-03-26 23:11:03

247

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Finding the infinite sum of a Fourier Series at a given $x$

Published on 26 Mar 2026 - 23:11

score 108 · Answer 2 · 2020-02-19 17:22:41

108

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$f(z)=(\log(1-z))^2$ and $\sum_{n=0}^{\infty} {a_n z^n} $ is the Taylor series of $f(z)$. Find $a_4$

Published on 19 Feb 2020 - 17:22

score 298 · Answer 3 · 2026-03-30 08:15:17

298

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$\sum_{n = 0}^\infty (-1)^n = \frac{1}{2}$ - Where have I gone wrong?

Published on 30 Mar 2026 - 8:15

score 22 · Answer 4 · 2020-02-21 10:23:06

How to prove that $\frac{k}{1-\beta^2}-\frac{k}{\sqrt{1-\beta^2}}=\frac{k\beta^2}{2}+O(\beta^4)$ for small $\beta$?

score 34 · Answer 5 · 2020-02-21 15:27:55

34

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Help identifying pattern in these number sequences for closed form Taylor Expansion

Published on 21 Feb 2020 - 15:27

score 259 · Answer 6 · 2026-03-29 06:30:10

259

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Taylor series expansion approximation

Published on 29 Mar 2026 - 6:30

score 52 · Answer 7 · 2026-03-25 11:05:19

52

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Sum involving 2nd antiderivative of the digamma function.

Published on 25 Mar 2026 - 11:05

score 66 · Answer 8 · 2020-02-22 20:33:09

66

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Expressing infinite product as a series (formalizing Euler's proof of Basel problem)

Published on 22 Feb 2020 - 20:33

score 745 · Answer 9 · 2020-02-22 22:53:24

745

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When is it acceptable to stop adding terms to a Taylor approximation if my goal it to find a limit?

Published on 22 Feb 2020 - 22:53

score 159 · Answer 10 · 2020-02-23 03:59:02

159

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How to expand $\sin (2z+1)$ in powers of $(z+1)$?

Published on 23 Feb 2020 - 3:59

score 224 · Answer 11 · 2026-03-31 18:25:44

224

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Is there a way of finding trigonometric ratios of any random angle between 0° to 90° without using a calculator?

Published on 31 Mar 2026 - 18:25

score 351 · Answer 12 · 2020-02-24 03:01:02

351

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$1-1+1-1+1-1+\cdots$ and $1-2+3-4+5-6+7-\cdots$ and Taylor's theorem

Published on 24 Feb 2020 - 3:01

score 219 · Answer 13 · 2026-03-31 04:17:20

219

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How can we get Nth digit of any irrational number in base 2 using Taylor expansion?

Published on 31 Mar 2026 - 4:17

score 83 · Answer 14 · 2020-02-25 03:50:21

83

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Taylor's Polynomial Evaluation

Published on 25 Feb 2020 - 3:50

score 4k · Answer 15 · 2026-03-26 22:14:01

4k

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Matrix exponential of sum of matrices

Published on 26 Mar 2026 - 22:14

List Question

Finding the infinite sum of a Fourier Series at a given $x$

$f(z)=(\log(1-z))^2$ and $\sum_{n=0}^{\infty} {a_n z^n} $ is the Taylor series of $f(z)$. Find $a_4$

$\sum_{n = 0}^\infty (-1)^n = \frac{1}{2}$ - Where have I gone wrong?

How to prove that $\frac{k}{1-\beta^2}-\frac{k}{\sqrt{1-\beta^2}}=\frac{k\beta^2}{2}+O(\beta^4)$ for small $\beta$?

Help identifying pattern in these number sequences for closed form Taylor Expansion

Taylor series expansion approximation

Sum involving 2nd antiderivative of the digamma function.

Expressing infinite product as a series (formalizing Euler's proof of Basel problem)

When is it acceptable to stop adding terms to a Taylor approximation if my goal it to find a limit?

How to expand $\sin (2z+1)$ in powers of $(z+1)$?

Is there a way of finding trigonometric ratios of any random angle between 0° to 90° without using a calculator?

$1-1+1-1+1-1+\cdots$ and $1-2+3-4+5-6+7-\cdots$ and Taylor's theorem

How can we get Nth digit of any irrational number in base 2 using Taylor expansion?

Taylor's Polynomial Evaluation

Matrix exponential of sum of matrices

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