Question

Closed form of a series (dilogarithm)

score 606 · Answer 1 · 2015-08-27 11:26:38

606

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Closed form of a series (dilogarithm)

Published on 27 Aug 2015 - 11:26

score 652 · Answer 2 · 2015-08-31 18:57:11

652

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Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

Published on 31 Aug 2015 - 18:57

score 684 · Answer 3 · 2015-09-04 15:56:40

684

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Calculating in closed form $\int_0^{\pi/2} \arctan\left(\sin ^3(x)\right) \, dx \ ?$

Published on 04 Sep 2015 - 15:56

score 884 · Answer 4 · 2015-09-06 20:27:10

884

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Conjecture $\Re\,\operatorname{Li}_2\left(\frac12+\frac i6\right)=\frac{7\pi^2}{48}-\frac13\arctan^22-\frac16\arctan^23-\frac18\ln^2(\tfrac{18}5)$

Published on 06 Sep 2015 - 20:27

score 866 · Answer 5 · 2026-03-25 14:25:14

866

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Conjecture $\int_0^1\frac{\ln^2\left(1+x+x^2\right)}x dx\stackrel?=\frac{2\pi}{9\sqrt3}\psi^{(1)}(\tfrac13)-\frac{4\pi^3}{27\sqrt3}-\frac23\zeta(3)$

Published on 25 Mar 2026 - 14:25

score 1.2k · Answer 6 · 2026-03-25 14:22:47

1.2k

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Integral ${\large\int}_0^1\ln^3\!\left(1+x+x^2\right)dx$

Published on 25 Mar 2026 - 14:22

score 205 · Answer 7 · 2015-09-10 03:56:46

205

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Evaluating a logarithmic integral in terms of trilogarithms

Published on 10 Sep 2015 - 3:56

score 111 · Answer 8 · 2015-09-10 05:02:38

111

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What is the integral of the square of a general polylogarithm with gaussian argument?

Published on 10 Sep 2015 - 5:02

score 6k · Answer 9 · 2015-09-10 14:21:43

6k

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Solve for $x,y$: $(3x)^{\log3} = (4y)^{\log4}$ and $4^{\log x} = 3^{\log y}$.

Published on 10 Sep 2015 - 14:21

score 972 · Answer 10 · 2026-03-25 10:56:03

972

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Conjectured closed form for $\operatorname{Li}_2\!\left(\sqrt{2-\sqrt3}\cdot e^{i\pi/12}\right)$

Published on 25 Mar 2026 - 10:56

score 289 · Answer 11 · 2015-09-15 08:48:15

289

Views

Simplification of an expression involving the dilogarithm with complex argument

Published on 15 Sep 2015 - 8:48

score 502 · Answer 12 · 2015-09-15 14:40:03

502

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Dilogarithm identity containing the tribonacci constant

Published on 15 Sep 2015 - 14:40

score 412 · Answer 13 · 2015-09-17 06:14:58

412

Views

Simplifying a certain polylogarithmic sum in two variables

Published on 17 Sep 2015 - 6:14

score 455 · Answer 14 · 2015-09-25 12:32:55

455

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A special value polylogarithm identity involving $\text{Li}_3(-1/2),\,\text{Li}_3(-1/3),\,\text{Li}_3(2/3),\,\text{Li}_2(-1/3),\,\text{Li}_2(2/3)$

Published on 25 Sep 2015 - 12:32

score 244 · Answer 15 · 2026-03-25 23:35:14

244

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closed form iterated logarithms

Published on 25 Mar 2026 - 23:35

List Question

Closed form of a series (dilogarithm)

Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

Calculating in closed form $\int_0^{\pi/2} \arctan\left(\sin ^3(x)\right) \, dx \ ?$

Conjecture $\Re\,\operatorname{Li}_2\left(\frac12+\frac i6\right)=\frac{7\pi^2}{48}-\frac13\arctan^22-\frac16\arctan^23-\frac18\ln^2(\tfrac{18}5)$

Conjecture $\int_0^1\frac{\ln^2\left(1+x+x^2\right)}x dx\stackrel?=\frac{2\pi}{9\sqrt3}\psi^{(1)}(\tfrac13)-\frac{4\pi^3}{27\sqrt3}-\frac23\zeta(3)$

Integral ${\large\int}_0^1\ln^3\!\left(1+x+x^2\right)dx$

Evaluating a logarithmic integral in terms of trilogarithms

What is the integral of the square of a general polylogarithm with gaussian argument?

Solve for $x,y$: $(3x)^{\log3} = (4y)^{\log4}$ and $4^{\log x} = 3^{\log y}$.

Conjectured closed form for $\operatorname{Li}_2\!\left(\sqrt{2-\sqrt3}\cdot e^{i\pi/12}\right)$

Simplification of an expression involving the dilogarithm with complex argument

Dilogarithm identity containing the tribonacci constant

Simplifying a certain polylogarithmic sum in two variables

A special value polylogarithm identity involving $\text{Li}_3(-1/2),\,\text{Li}_3(-1/3),\,\text{Li}_3(2/3),\,\text{Li}_2(-1/3),\,\text{Li}_2(2/3)$

closed form iterated logarithms

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