List questions from closed-form

Published on 22 Oct 2019 - 20:19

190

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Closed form solution of $x + \sin(x) = k$

Published on 23 Oct 2019 - 20:06

452

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Finding a closed form for (a) $\sum_{k=0}^n 4^k {2n \choose 2k}$

Published on 23 Oct 2019 - 23:14

94

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Series representation for $(1+x)^{n-m}(1-x)^{m}$

Published on 26 Oct 2019 - 18:45

133

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Show that $ \int_0^\pi \cot(x)\arctan(\tanh\pi(\tan(x))) \mathrm{d}x=\pi \log(3)$

Published on 27 Oct 2019 - 13:57

179

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Closed-form solvability of elementary transcendental equations?

Published on 17 Mar 2026 - 19:15

332

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Closed Form for $\sum\limits_{n=-2a}^\infty(n+a){2a\choose-n}^4$

Published on 28 Oct 2019 - 7:10

1.5k

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Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$

Published on 26 Mar 2026 - 1:11

263

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Possible to get a closed form expression, or an upper bound, for $ f(n)=\sum_{m=1}^\infty \bigg(\frac{m+n}{3}\bigg)^{m+n}\bigg(\frac{1}{m}\bigg)^m$?

Published on 29 Oct 2019 - 11:57

197

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Simplifying a 'fractal-like' expression with tetration

Published on 25 Mar 2026 - 14:43

176

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Closed form for $\int_{0}^1 \frac{\ln(x)\ln(1-x)^b}{x^2}dx$

Published on 26 Mar 2026 - 22:54

68

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Closed form solution of a sum in a sum

Published on 02 Nov 2019 - 23:16

17

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General formula for the following operator?

Published on 03 Nov 2019 - 16:13

121

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Closed Form for $\int_{0}^1\frac{\ln(x)\ln^a(1-x)}{x^3}dx$

Published on 26 Mar 2026 - 22:54

142

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Solve a recurrence that has two forms for $n$ even or odd

Published on 28 Mar 2026 - 20:04

List Question

$\int \frac{\sin x}{1+2\sin x}dx$

Closed form solution of $x + \sin(x) = k$

Finding a closed form for (a) $\sum_{k=0}^n 4^k {2n \choose 2k}$

Series representation for $(1+x)^{n-m}(1-x)^{m}$

Show that $ \int_0^\pi \cot(x)\arctan(\tanh\pi(\tan(x))) \mathrm{d}x=\pi \log(3)$

Closed-form solvability of elementary transcendental equations?

Closed Form for $\sum\limits_{n=-2a}^\infty(n+a){2a\choose-n}^4$

Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$

Possible to get a closed form expression, or an upper bound, for $ f(n)=\sum_{m=1}^\infty \bigg(\frac{m+n}{3}\bigg)^{m+n}\bigg(\frac{1}{m}\bigg)^m$?

Simplifying a 'fractal-like' expression with tetration

Closed form for $\int_{0}^1 \frac{\ln(x)\ln(1-x)^b}{x^2}dx$

Closed form solution of a sum in a sum

General formula for the following operator?

Closed Form for $\int_{0}^1\frac{\ln(x)\ln^a(1-x)}{x^3}dx$

Solve a recurrence that has two forms for $n$ even or odd

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