Question

Is there a positive integer $N$ for which $\sum_{n=1}^N \cos\left(n^2x\right)=0$ for every $x\in[0,2\pi]$?

score 103 · Answer 1 · 2021-10-08 08:00:15

103

Views

Is there a positive integer $N$ for which $\sum_{n=1}^N \cos\left(n^2x\right)=0$ for every $x\in[0,2\pi]$?

Published on 08 Oct 2021 - 8:00

score 71 · Answer 2 · 2021-10-11 09:28:26

71

Views

Solve definite integral of infinite series of a complex function

Published on 11 Oct 2021 - 9:28

score 134 · Answer 3 · 2021-10-13 09:43:10

134

Views

Simplify infinitely recursive function $f(a,b) = a+b\sin( a + b\sin( \cdots ( a + b\sin(a) ) \cdots ) )$

Published on 13 Oct 2021 - 9:43

score 799 · Answer 4 · 2021-10-18 02:54:11

799

Views

Is $\sum_{a=0}^m\sum_{b=0}^n\cos(abx)$ always positive?

Published on 18 Oct 2021 - 2:54

score 139 · Answer 5 · 2026-03-26 17:53:37

139

Views

Apply the Abel summation formula to $\sum_{i=1}^k \operatorname{sinc} \bigl( \pi (x-i p) \bigr)$

Published on 26 Mar 2026 - 17:53

score 180 · Answer 6 · 2021-10-22 15:59:23

180

Views

$\cos(\cos(\cos(\cos(\cos(\cos(\cos(....(\theta)))))))))$ approaches a constant as the number of cosines increases

Published on 22 Oct 2021 - 15:59

score 128 · Answer 7 · 2026-02-24 08:34:33

128

Views

How to calculate the inverse of $f(t) = \frac{(k/2)(\sin(t) + t) - t}{2π (k/2 - 1)}$?

Published on 24 Feb 2026 - 8:34

score 216 · Answer 8 · 2021-11-02 10:58:33

216

Views

Proof of series expansion of $\operatorname{arctanh}(e^{is})$ for $s\in(0,\pi)$.

Published on 02 Nov 2021 - 10:58

score 493 · Answer 9 · 2021-11-05 10:21:31

493

Views

$\sum _{k=1}^n\:\left(\cos\left(\frac{2\cdot k\cdot \pi }{n}\right)-2\:+\:i\cdot \sin\left(\frac{2\cdot k\cdot \pi }{n}\right)\right)$

Published on 05 Nov 2021 - 10:21

score 105 · Answer 10 · 2021-11-07 13:19:12

105

Views

How to calculate sums like $\sum_{n=2}^{\infty} \frac{ sinc (-4 \cdot \pi (n-3)(n-4) ) }{n(n-1)} $ with the Residue Theorem?

Published on 07 Nov 2021 - 13:19

score 71 · Answer 11 · 2021-11-13 08:04:24

71

Views

Trigonometric terms for floor function $Q_k(n)$

Published on 13 Nov 2021 - 8:04

score 231 · Answer 12 · 2021-12-11 13:01:15

231

Views

What is known about sums of the form $\sum_{n=-\infty}^{\infty} \operatorname{sinc} (n^{p})$?

Published on 11 Dec 2021 - 13:01

score 39 · Answer 13 · 2021-12-13 22:10:34

39

Views

Is my assumption in levy bending plates right?

Published on 13 Dec 2021 - 22:10

score 81 · Answer 14 · 2021-12-25 03:17:37

81

Views

Sinusoids as solutions to differential equations

Published on 25 Dec 2021 - 3:17

score 47 · Answer 15 · 2022-01-13 18:33:39

47

Views

Finding a periodic function with this fundamental cycle

Published on 13 Jan 2022 - 18:33

List Question

Is there a positive integer $N$ for which $\sum_{n=1}^N \cos\left(n^2x\right)=0$ for every $x\in[0,2\pi]$?

Solve definite integral of infinite series of a complex function

Simplify infinitely recursive function $f(a,b) = a+b\sin( a + b\sin( \cdots ( a + b\sin(a) ) \cdots ) )$

Is $\sum_{a=0}^m\sum_{b=0}^n\cos(abx)$ always positive?

Apply the Abel summation formula to $\sum_{i=1}^k \operatorname{sinc} \bigl( \pi (x-i p) \bigr)$

$\cos(\cos(\cos(\cos(\cos(\cos(\cos(....(\theta)))))))))$ approaches a constant as the number of cosines increases

How to calculate the inverse of $f(t) = \frac{(k/2)(\sin(t) + t) - t}{2π (k/2 - 1)}$?

Proof of series expansion of $\operatorname{arctanh}(e^{is})$ for $s\in(0,\pi)$.

$\sum _{k=1}^n\:\left(\cos\left(\frac{2\cdot k\cdot \pi }{n}\right)-2\:+\:i\cdot \sin\left(\frac{2\cdot k\cdot \pi }{n}\right)\right)$

How to calculate sums like $\sum_{n=2}^{\infty} \frac{ sinc (-4 \cdot \pi (n-3)(n-4) ) }{n(n-1)} $ with the Residue Theorem?

Trigonometric terms for floor function $Q_k(n)$

What is known about sums of the form $\sum_{n=-\infty}^{\infty} \operatorname{sinc} (n^{p})$?

Is my assumption in levy bending plates right?

Sinusoids as solutions to differential equations

Finding a periodic function with this fundamental cycle

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