Question

Inverse of the polylogarithm

score 3.1k · Answer 1 · 2011-10-18 01:18:29

3.1k

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Inverse of the polylogarithm

Published on 18 Oct 2011 - 1:18

score 688 · Answer 2 · 2013-02-03 16:27:01

688

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Computing the value of $\operatorname{Li}_{3}\left(\frac{1}{2} \right) $

Published on 03 Feb 2013 - 16:27

score 96 · Answer 3 · 2020-08-02 09:10:48

96

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On $\int_0^{2\pi }\frac{\prod_{k=1}^m \text{Li}_{a_k}(e^{-ix})-\prod_{k=1}^m \text{Li}_{a_k}(e^{ix})}{e^{-ix}-e^{ix}} \, dx$

Published on 02 Aug 2020 - 9:10

score 397 · Answer 4 · 2020-08-04 09:22:58

397

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How can I evaluate $\int _0^1\frac{\text{Li}_2\left(-x\right)\ln \left(1-x\right)}{1+x}\:dx$

Published on 04 Aug 2020 - 9:22

score 405 · Answer 5 · 2020-08-06 04:51:59

405

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How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^3\left(1+x\right)}{1+x}\:dx$

Published on 06 Aug 2020 - 4:51

score 928 · Answer 6 · 2020-08-07 13:27:55

928

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Evaluating $\int_0^1\frac{\arctan x\ln\left(\frac{2x^2}{1+x^2}\right)}{1-x}dx$

Published on 07 Aug 2020 - 13:27

score 279 · Answer 7 · 2020-08-09 10:45:34

279

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Is there a closed form without MZV for $ \sum _{k=1}^{\infty }\frac{H_k}{k^6\:2^k}$?

Published on 09 Aug 2020 - 10:45

score 680 · Answer 8 · 2020-08-16 19:06:49

680

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How can you approach $\int_0^{\pi/2} x\frac{\ln(\cos x)}{\sin x}dx$

Published on 16 Aug 2020 - 19:06

score 702 · Answer 9 · 2020-08-18 08:24:38

702

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How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Published on 18 Aug 2020 - 8:24

score 589 · Answer 10 · 2026-03-25 23:37:51

589

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How to evaluate $\int_0^{\pi/2} x\ln^2(\sin x)\textrm{d}x$ in a different way?

Published on 25 Mar 2026 - 23:37

score 677 · Answer 11 · 2020-08-20 16:02:58

677

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How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^5\left(1+x\right)}{1+x}\:dx$

Published on 20 Aug 2020 - 16:02

score 1k · Answer 12 · 2020-08-20 16:36:36

1k

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How to approach $\sum _{n=1}^{\infty } \frac{16^n}{n^4 \binom{2 n}{n}^2}$?

Published on 20 Aug 2020 - 16:36

score 729 · Answer 13 · 2020-08-26 00:42:27

729

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How to find $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{n^3}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}^{(2)}}{n^2}$ using real methods?

Published on 26 Aug 2020 - 0:42

score 331 · Answer 14 · 2020-08-28 04:16:57

331

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How to approach $\sum_{n=0}^\infty(-1)^n\frac{H_{2n+1}}{(2n+1)^3}$ elegantly?

Published on 28 Aug 2020 - 4:16

score 302 · Answer 15 · 2020-08-28 17:16:02

302

Views

Does there exist a closed form for $\int_0^{\pi/2}\frac{x^2\ \text{Li}_2(\sin^2x)}{\sin x}dx$?

Published on 28 Aug 2020 - 17:16

List Question

Inverse of the polylogarithm

Computing the value of $\operatorname{Li}_{3}\left(\frac{1}{2} \right) $

On $\int_0^{2\pi }\frac{\prod_{k=1}^m \text{Li}_{a_k}(e^{-ix})-\prod_{k=1}^m \text{Li}_{a_k}(e^{ix})}{e^{-ix}-e^{ix}} \, dx$

How can I evaluate $\int _0^1\frac{\text{Li}_2\left(-x\right)\ln \left(1-x\right)}{1+x}\:dx$

How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^3\left(1+x\right)}{1+x}\:dx$

Evaluating $\int_0^1\frac{\arctan x\ln\left(\frac{2x^2}{1+x^2}\right)}{1-x}dx$

Is there a closed form without MZV for $ \sum _{k=1}^{\infty }\frac{H_k}{k^6\:2^k}$?

How can you approach $\int_0^{\pi/2} x\frac{\ln(\cos x)}{\sin x}dx$

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

How to evaluate $\int_0^{\pi/2} x\ln^2(\sin x)\textrm{d}x$ in a different way?

How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^5\left(1+x\right)}{1+x}\:dx$

How to approach $\sum _{n=1}^{\infty } \frac{16^n}{n^4 \binom{2 n}{n}^2}$?

How to find $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{n^3}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}^{(2)}}{n^2}$ using real methods?

How to approach $\sum_{n=0}^\infty(-1)^n\frac{H_{2n+1}}{(2n+1)^3}$ elegantly?

Does there exist a closed form for $\int_0^{\pi/2}\frac{x^2\ \text{Li}_2(\sin^2x)}{\sin x}dx$?

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