List questions from closed-form

Published on 27 Mar 2026 - 18:49

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Closed form for $\int_0^{\infty}\sin(x^n)\mathbb{d}x$

Published on 30 Nov 2015 - 4:26

275

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The elliptic integral $\frac{K'}{K}=\sqrt{2}-1$ is known in closed form?

Published on 31 Mar 2026 - 8:14

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Integral $\int_0^\infty\operatorname{arccot}(x)\,\operatorname{arccot}(2x)\,\operatorname{arccot}(5x)\,dx$

Published on 01 Dec 2015 - 0:34

61

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need help in finding closed form for $\sum_{i=0}^{\log(n/2)} \frac{n}{2^i}\log\frac{n}{2^i}$

Published on 01 Dec 2015 - 15:55

559

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Why is this definite integral antisymmetric in $s\mapsto s^{-1}$?

Published on 29 Mar 2026 - 12:41

198

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What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?

Published on 09 Dec 2015 - 21:58

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Closed formula for the power series

Published on 10 Dec 2015 - 15:26

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Find an explicit formula for a sequence

Published on 13 Dec 2015 - 16:20

191

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How to solve in radicals this family of equations for any degree $k$?

Published on 18 Dec 2015 - 13:19

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For $n\geq 1$, $\sum_{k=0}^{\infty}\frac{(-1)^{k}(nk+1)^{3}}{(k+1)^6}$ in terms of $\zeta(3)$ and $\zeta(5)$ from a series calculator. Is possible?

Published on 18 Dec 2015 - 13:52

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Integral $\int_0^\infty\frac{\tanh^2(x)}{x^2}dx$

Published on 28 Mar 2026 - 18:16

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Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function

Published on 22 Dec 2015 - 5:01

271

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Can one find a closed form solution to $\ln x=\frac{1}{x}$,

Published on 27 Mar 2026 - 7:14

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Closed formula for sum of increasing exponents

Published on 23 Dec 2015 - 17:22

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Another polylog integral

Closed form for $\int_0^{\infty}\sin(x^n)\mathbb{d}x$

The elliptic integral $\frac{K'}{K}=\sqrt{2}-1$ is known in closed form?

Integral $\int_0^\infty\operatorname{arccot}(x)\,\operatorname{arccot}(2x)\,\operatorname{arccot}(5x)\,dx$

need help in finding closed form for $\sum_{i=0}^{\log(n/2)} \frac{n}{2^i}\log\frac{n}{2^i}$

Why is this definite integral antisymmetric in $s\mapsto s^{-1}$?

What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?

Closed formula for the power series

Find an explicit formula for a sequence

How to solve in radicals this family of equations for any degree $k$?

For $n\geq 1$, $\sum_{k=0}^{\infty}\frac{(-1)^{k}(nk+1)^{3}}{(k+1)^6}$ in terms of $\zeta(3)$ and $\zeta(5)$ from a series calculator. Is possible?

Integral $\int_0^\infty\frac{\tanh^2(x)}{x^2}dx$

Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function

Can one find a closed form solution to $\ln x=\frac{1}{x}$,

Closed formula for sum of increasing exponents

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