Question

Evaluation of the sum $\sum\limits_{n=1}^{\infty}\frac1n\sin\frac1n$

score 224 · Answer 1 · 2026-03-25 23:39:09

224

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Evaluation of the sum $\sum\limits_{n=1}^{\infty}\frac1n\sin\frac1n$

Published on 25 Mar 2026 - 23:39

score 549 · Answer 2 · 2019-03-02 14:26:22

549

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Closed form for these polynomials?

Published on 02 Mar 2019 - 14:26

score 30 · Answer 3 · 2026-03-25 21:47:58

30

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How to prove that a recursive function with inner summation is approximately equal to some closed-form equation?

Published on 25 Mar 2026 - 21:47

score 81 · Answer 4 · 2026-03-25 03:04:08

81

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Hamiltonian paths and cycles of rook graph on $n\times2$ chessboard

Published on 25 Mar 2026 - 3:04

score 66 · Answer 5 · 2019-03-03 19:04:23

66

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How to find a closed form for $\sum_{i=0}^n \binom{a+i}{b+i}i$

Published on 03 Mar 2019 - 19:04

score 95 · Answer 6 · 2026-03-25 14:28:52

95

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Formula for this diminishing function

Published on 25 Mar 2026 - 14:28

score 109 · Answer 7 · 2026-03-25 22:11:23

109

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Does $\sum\limits_{k=2}^{\infty}{\frac{|B_{k}|}{k!}(\cos(n)-1)}$ have a closed form?

Published on 25 Mar 2026 - 22:11

score 60 · Answer 8 · 2019-03-06 17:29:00

60

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Interesting polynomial: $R_{k+1}(x)=x(2^{-2k-1}-1)\zeta(2k+2)+\int_0^x\int_0^t R_{k}(u)dudt$

Published on 06 Mar 2019 - 17:29

score 68 · Answer 9 · 2019-03-07 19:46:04

68

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Solving $\int_0^x\int_u^{u+1}\frac1{\ln t}\,dt\,du=0$ (an extension to the Ramanujan-Soldner constant)

Published on 07 Mar 2019 - 19:46

score 73 · Answer 10 · 2019-03-10 19:05:36

73

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What is and what isn't a "closed form solution"

Published on 10 Mar 2019 - 19:05

score 122 · Answer 11 · 2026-03-26 00:52:49

122

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Simplifying $\prod\limits_{k\neq j=0}^{n-1}\frac1{\lambda_{n,k}-\lambda_{n,j}}$ for $\lambda_{n,k}=\exp\frac{i\pi(2k+1)}{n}$

Published on 26 Mar 2026 - 0:52

score 208 · Answer 12 · 2019-03-14 15:35:23

208

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Is it true that $(a^2-ab+b^2)(c^2-cd+d^2)=h^2-hk+k^2$ for some coprime $h$ and $k$?

Published on 14 Mar 2019 - 15:35

score 162 · Answer 13 · 2019-03-14 16:10:50

162

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Solve the recurrence $b_1 = 2$ for $b_n = 3b_{n-1} + 5$

Published on 14 Mar 2019 - 16:10

score 149 · Answer 14 · 2019-03-16 11:18:42

149

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How to handle a differential equation whose RHS contains the derivative of the Dirac delta function?

Published on 16 Mar 2019 - 11:18

score 382 · Answer 15 · 2019-03-19 17:33:16

382

Views

Evaluating a Polynomic-Trigonometric-Hyperbolic Integral

Published on 19 Mar 2019 - 17:33

List Question

Evaluation of the sum $\sum\limits_{n=1}^{\infty}\frac1n\sin\frac1n$

Closed form for these polynomials?

How to prove that a recursive function with inner summation is approximately equal to some closed-form equation?

Hamiltonian paths and cycles of rook graph on $n\times2$ chessboard

How to find a closed form for $\sum_{i=0}^n \binom{a+i}{b+i}i$

Formula for this diminishing function

Does $\sum\limits_{k=2}^{\infty}{\frac{|B_{k}|}{k!}(\cos(n)-1)}$ have a closed form?

Interesting polynomial: $R_{k+1}(x)=x(2^{-2k-1}-1)\zeta(2k+2)+\int_0^x\int_0^t R_{k}(u)dudt$

Solving $\int_0^x\int_u^{u+1}\frac1{\ln t}\,dt\,du=0$ (an extension to the Ramanujan-Soldner constant)

What is and what isn't a "closed form solution"

Simplifying $\prod\limits_{k\neq j=0}^{n-1}\frac1{\lambda_{n,k}-\lambda_{n,j}}$ for $\lambda_{n,k}=\exp\frac{i\pi(2k+1)}{n}$

Is it true that $(a^2-ab+b^2)(c^2-cd+d^2)=h^2-hk+k^2$ for some coprime $h$ and $k$?

Solve the recurrence $b_1 = 2$ for $b_n = 3b_{n-1} + 5$

How to handle a differential equation whose RHS contains the derivative of the Dirac delta function?

Evaluating a Polynomic-Trigonometric-Hyperbolic Integral

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