Question

Closed form for the $n$-th derivative of $\csc^2$?

score 161 · Answer 1 · 2023-12-01 17:00:35

161

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Closed form for the $n$-th derivative of $\csc^2$?

Published on 01 Dec 2023 - 17:00

score 92 · Answer 2 · 2023-12-02 14:42:48

92

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Evaluate $\sum_{m=1}^{\infty} \frac{(-1)^m \mathcal{H}_{2m} }{2m+1} - \frac{1}{2} \sum_ {m=1}^{\infty} \frac{(-1)^m \mathcal{H}_m}{2m+1}$

Published on 02 Dec 2023 - 14:42

score 87 · Answer 3 · 2026-03-27 17:06:21

87

Views

Symplectic area is invariant under homotopy

Published on 27 Mar 2026 - 17:06

score 232 · Answer 4 · 2023-12-05 10:02:48

232

Views

Evaluate $\int_{0}^{1}\{1/x\}^2\,dx$

Published on 05 Dec 2023 - 10:02

score 163 · Answer 5 · 2023-12-05 10:46:05

163

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Double integral $\int_{0}^{1}\int_{0}^{1}\frac{x^{a-1}y^{b-1}}{(1+xy)\ln(xy)}\,dx\,dy$

Published on 05 Dec 2023 - 10:46

score 28 · Answer 6 · 2026-03-28 06:59:49

28

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Finding $\sin(a+b)^{2k} = \sum a_i \sin^{2 n_i}(b_i a) \cos^{2 m_i}(c_i a) \sin^{2 l_i}(d_i b) \cos^{2 j_i}(e_i b)$

Published on 28 Mar 2026 - 6:59

score 83 · Answer 7 · 2026-03-25 23:35:08

83

Views

How can i solve this optimization problem effectively?

Published on 25 Mar 2026 - 23:35

score 136 · Answer 8 · 2023-12-05 17:26:15

136

Views

Evaluate $\int_{0}^{\pi/2}x\ln\left(\tan x\right)\,dx$

Published on 05 Dec 2023 - 17:26

score 81 · Answer 9 · 2023-12-06 10:25:03

81

Views

Closed form solution of convex conjugate of $|1 - x^{a} |^{\frac{1}{a}} + \iota_{[0, \infty)}(x)$

Published on 06 Dec 2023 - 10:25

score 138 · Answer 10 · 2023-12-06 11:02:50

138

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Evaluate $\int_{0}^{\infty} \frac{x^2 + \sin(\pi x)}{1 + \exp(\pi x)} \,dx$

Published on 06 Dec 2023 - 11:02

score 159 · Answer 11 · 2026-03-25 14:22:53

159

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Does a closed-form expression exist for $ \int_0^\infty \ln(x) \operatorname{sech}(x)^n dx $?

Published on 25 Mar 2026 - 14:22

score 50 · Answer 12 · 2023-12-09 08:20:51

50

Views

How do today's solvers solve the closed solution of a system of equations

Published on 09 Dec 2023 - 8:20

score 194 · Answer 13 · 2026-03-28 10:24:14

194

Views

Which closed form expression for this series involving Catalan numbers : $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{4^nn^2}\binom{2n}{n}$

Published on 28 Mar 2026 - 10:24

score 205 · Answer 14 · 2026-02-23 12:04:16

205

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$e$ is hidden in Pascal's (binomial) triangle. What is hidden in the trinomial triangle, in the same way?

Published on 23 Feb 2026 - 12:04

score 46 · Answer 15 · 2026-03-28 15:36:43

46

Views

Is there really no simple form for the projection onto the positive part of the hyperboloid model?

Published on 28 Mar 2026 - 15:36

List Question

Closed form for the $n$-th derivative of $\csc^2$?

Evaluate $\sum_{m=1}^{\infty} \frac{(-1)^m \mathcal{H}_{2m} }{2m+1} - \frac{1}{2} \sum_ {m=1}^{\infty} \frac{(-1)^m \mathcal{H}_m}{2m+1}$

Symplectic area is invariant under homotopy

Evaluate $\int_{0}^{1}\{1/x\}^2\,dx$

Double integral $\int_{0}^{1}\int_{0}^{1}\frac{x^{a-1}y^{b-1}}{(1+xy)\ln(xy)}\,dx\,dy$

Finding $\sin(a+b)^{2k} = \sum a_i \sin^{2 n_i}(b_i a) \cos^{2 m_i}(c_i a) \sin^{2 l_i}(d_i b) \cos^{2 j_i}(e_i b)$

How can i solve this optimization problem effectively?

Evaluate $\int_{0}^{\pi/2}x\ln\left(\tan x\right)\,dx$

Closed form solution of convex conjugate of $|1 - x^{a} |^{\frac{1}{a}} + \iota_{[0, \infty)}(x)$

Evaluate $\int_{0}^{\infty} \frac{x^2 + \sin(\pi x)}{1 + \exp(\pi x)} \,dx$

Does a closed-form expression exist for $ \int_0^\infty \ln(x) \operatorname{sech}(x)^n dx $?

How do today's solvers solve the closed solution of a system of equations

Which closed form expression for this series involving Catalan numbers : $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{4^nn^2}\binom{2n}{n}$

$e$ is hidden in Pascal's (binomial) triangle. What is hidden in the trinomial triangle, in the same way?

Is there really no simple form for the projection onto the positive part of the hyperboloid model?

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