Question

Sum with harmonic number of squared argument as e.g. $\sum_{k=1}^\infty \frac{H(k^2)}{k^2}$

score 78 · Answer 1 · 2026-03-25 11:03:45

78

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Sum with harmonic number of squared argument as e.g. $\sum_{k=1}^\infty \frac{H(k^2)}{k^2}$

Published on 25 Mar 2026 - 11:03

score 2.2k · Answer 2 · 2019-01-12 15:41:37

2.2k

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Integral $\int_0^\frac{\pi}{2} x^2\sqrt{\tan x}\,\mathrm dx$

Published on 12 Jan 2019 - 15:41

score 97 · Answer 3 · 2019-01-13 18:38:58

97

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Find closed form of sum of fraction of binomial coefficients

Published on 13 Jan 2019 - 18:38

score 198 · Answer 4 · 2026-03-25 09:28:21

198

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Studying on this sum interesting $\sum_{n=1}^{\infty}\frac{{2n \choose n }}{4^n n}$

Published on 25 Mar 2026 - 9:28

score 1.3k · Answer 5 · 2026-03-25 07:58:35

1.3k

Views

Evaluating Dirichlet $L$-functions at $s=1$

Published on 25 Mar 2026 - 7:58

score 418 · Answer 6 · 2026-03-25 21:54:07

418

Views

Closed Form of the Real Portion of $f(n) = \prod_{m=2}^{n-1} e^{\pi i n/m}$

Published on 25 Mar 2026 - 21:54

score 126 · Answer 7 · 2019-01-17 10:28:10

126

Views

Is there a closed-form formula for the derivative of the orthogonal polar factor of a matrix?

Published on 17 Jan 2019 - 10:28

score 78 · Answer 8 · 2019-01-18 09:51:04

How to find the closed form of the recursive equation, if 2 of the 3 roots of the characteristic equation are imaginary and only 1 root is real?

score 187 · Answer 9 · 2019-01-20 22:25:37

187

Views

Conjecture: $\sum\limits_{n\geq0}\left(\frac12\right)^n\prod\limits_{k=1}^{n}\frac{2n-2k+1}{2n-2k+2}=\sqrt2$

Published on 20 Jan 2019 - 22:25

score 61 · Answer 10 · 2019-01-20 23:39:12

61

Views

$ t(n) = t( x_1 x_2 x_3 ...) = t(x_1) + t(x_2) + t(x_3) + ... + t( x_1 + x_2 + x_3 + ... ) $

Published on 20 Jan 2019 - 23:39

score 81 · Answer 11 · 2026-03-25 14:03:25

81

Views

Closed-form solution for $f(x)/x=y$ using $f^{-1}$

Published on 25 Mar 2026 - 14:03

score 181 · Answer 12 · 2019-01-21 19:36:28

181

Views

∫ sin(sin(x)) dx as a "suitably generalized Kampé de Fériet hypergeometric function of two variables"

Published on 21 Jan 2019 - 19:36

score 260 · Answer 13 · 2026-02-23 02:42:17

260

Views

Given a differential form $\omega$, is there a differential form $\phi$ such that $\omega\wedge\phi$ is closed?

Published on 23 Feb 2026 - 2:42

score 119 · Answer 14 · 2019-01-24 23:02:36

119

Views

Is it possible to find a closed form using modular arithmetic?

Published on 24 Jan 2019 - 23:02

score 149 · Answer 15 · 2019-01-24 23:46:25

149

Views

About $ f(x^2) = f(x) + f(x/2) $

Published on 24 Jan 2019 - 23:46

List Question

Sum with harmonic number of squared argument as e.g. $\sum_{k=1}^\infty \frac{H(k^2)}{k^2}$

Integral $\int_0^\frac{\pi}{2} x^2\sqrt{\tan x}\,\mathrm dx$

Find closed form of sum of fraction of binomial coefficients

Studying on this sum interesting $\sum_{n=1}^{\infty}\frac{{2n \choose n }}{4^n n}$

Evaluating Dirichlet $L$-functions at $s=1$

Closed Form of the Real Portion of $f(n) = \prod_{m=2}^{n-1} e^{\pi i n/m}$

Is there a closed-form formula for the derivative of the orthogonal polar factor of a matrix?

How to find the closed form of the recursive equation, if 2 of the 3 roots of the characteristic equation are imaginary and only 1 root is real?

Conjecture: $\sum\limits_{n\geq0}\left(\frac12\right)^n\prod\limits_{k=1}^{n}\frac{2n-2k+1}{2n-2k+2}=\sqrt2$

$ t(n) = t( x_1 x_2 x_3 ...) = t(x_1) + t(x_2) + t(x_3) + ... + t( x_1 + x_2 + x_3 + ... ) $

Closed-form solution for $f(x)/x=y$ using $f^{-1}$

∫ sin(sin(x)) dx as a "suitably generalized Kampé de Fériet hypergeometric function of two variables"

Given a differential form $\omega$, is there a differential form $\phi$ such that $\omega\wedge\phi$ is closed?

Is it possible to find a closed form using modular arithmetic?

About $ f(x^2) = f(x) + f(x/2) $

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