List questions from closed-form

Published on 15 Apr 2020 - 7:25

91

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Nice integral $\Im\Big(\int_{0}^{1}\ln\Big(\arctan\Big(\frac{x^2-x-1}{x^2+x+1}\Big)\Big)dx\Big)=\pi$

Published on 30 Mar 2026 - 5:26

112

Views

How to evaluate the integral $\int_{-1}^{0}\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{\cdots\sqrt{1+x}}}}}dx=?$

Published on 28 Mar 2026 - 11:43

128

Views

Recurrence Relation: Hᵥ = 2ᵛ - Hᵥ₋₁

Published on 30 Mar 2026 - 6:48

103

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Closed form for the infinite product $S_n=\Pi_{i=1}^{\infty} (1+\frac{1}{2^i})$

Published on 28 Mar 2026 - 22:38

77

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What is the closed form of $\sum_{l=1}^\infty \left(1 -\frac{l}{\sqrt{l^2 + a^2}}\right) $?

Published on 20 Apr 2020 - 16:59

273

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Calculate the closed formula of a series

Published on 30 Mar 2026 - 8:14

366

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Evaluate $\int_0^1 \frac{x \operatorname{Li}_2(x) \log (1+x)}{x^2+1} \, dx$

Published on 26 Mar 2026 - 13:02

431

Views

Do the floor and ceiling functions count as closed-form expressions?

Published on 29 Mar 2026 - 6:28

126

Views

Is there a way to simplify the solution to $\int_{1}^{e^{\frac{1}{e}}} x^{x^{x^{x^{...}}}} dx$

Published on 25 Mar 2026 - 22:26

295

Views

Computing $\int_0^1\frac{1-2x}{2x^2-2x+1}\ln(x)\text{Li}_2(x)dx$

Published on 26 Mar 2026 - 13:02

410

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Integrating the product of lines.

Published on 30 Mar 2026 - 11:37

332

Views

Closed form of recurrence relation $a_k=(n+k)a_{k-1}-ka_{k-2}$

Published on 03 May 2020 - 19:23

312

Views

Closed form expression for parallel transport / Bishop Frame along a cubic Bezier curve?

Published on 26 Mar 2026 - 3:11

267

Views

Find a closed form to the solution of $\sqrt{2-\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2-x}}}}}=x$

Published on 23 Feb 2026 - 6:39

List Question

How to solve recurrences related to factorials?

Nice integral $\Im\Big(\int_{0}^{1}\ln\Big(\arctan\Big(\frac{x^2-x-1}{x^2+x+1}\Big)\Big)dx\Big)=\pi$

How to evaluate the integral $\int_{-1}^{0}\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{\cdots\sqrt{1+x}}}}}dx=?$

Recurrence Relation: Hᵥ = 2ᵛ - Hᵥ₋₁

Closed form for the infinite product $S_n=\Pi_{i=1}^{\infty} (1+\frac{1}{2^i})$

What is the closed form of $\sum_{l=1}^\infty \left(1 -\frac{l}{\sqrt{l^2 + a^2}}\right) $?

Calculate the closed formula of a series

Evaluate $\int_0^1 \frac{x \operatorname{Li}_2(x) \log (1+x)}{x^2+1} \, dx$

Do the floor and ceiling functions count as closed-form expressions?

Is there a way to simplify the solution to $\int_{1}^{e^{\frac{1}{e}}} x^{x^{x^{x^{...}}}} dx$

Computing $\int_0^1\frac{1-2x}{2x^2-2x+1}\ln(x)\text{Li}_2(x)dx$

Integrating the product of lines.

Closed form of recurrence relation $a_k=(n+k)a_{k-1}-ka_{k-2}$

Closed form expression for parallel transport / Bishop Frame along a cubic Bezier curve?

Find a closed form to the solution of $\sqrt{2-\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2-x}}}}}=x$

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