Question

Converting an integrand into a polylog?

score 117 · Answer 1 · 2015-05-28 18:25:56

117

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Converting an integrand into a polylog?

Published on 28 May 2015 - 18:25

score 626 · Answer 2 · 2015-06-04 23:01:23

626

Views

The log integrals $\int_{0}^{1/2} \frac{\log(1+2x) \log(x)}{1+x} \, dx $ and $ \int_{0}^{1/2} \frac{\log(1+2x) \log(1-x)}{1+x} \, dx$

Published on 04 Jun 2015 - 23:01

score 111 · Answer 3 · 2015-06-05 00:53:37

111

Views

Equality with dilogarithms

Published on 05 Jun 2015 - 0:53

score 325 · Answer 4 · 2015-06-18 05:45:37

325

Views

Understanding limits for the polylogarithmic function

Published on 18 Jun 2015 - 5:45

score 1k · Answer 5 · 2015-06-27 15:25:23

1k

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About the integral $\int_{0}^{1}\frac{\log(x)\log^2(1+x)}{x}\,dx$

Published on 27 Jun 2015 - 15:25

score 599 · Answer 6 · 2015-07-25 03:04:27

599

Views

A conjectured identity for tetralogarithms $\operatorname{Li}_4$

Published on 25 Jul 2015 - 3:04

score 3.7k · Answer 7 · 2015-07-27 22:43:51

3.7k

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A difficult logarithmic integral ${\Large\int}_0^1\log(x)\,\log(2+x)\,\log(1+x)\,\log\left(1+x^{-1}\right)dx$

Published on 27 Jul 2015 - 22:43

score 585 · Answer 8 · 2015-07-31 10:46:52

585

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Closed-form of $\int\limits_0^1\left(\frac{\left(x^2+1\right)\arcsin(x)}{\sqrt{1-x^2}}+2x\ln\left(x^2+1\right)\right)\frac{\ln x}{x^3+x}\,dx$

Published on 31 Jul 2015 - 10:46

score 1.3k · Answer 9 · 2015-08-02 02:16:58

1.3k

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Integral $\int_0^\infty\text{Li}_2\left(e^{-\pi x}\right)\arctan x\,dx$

Published on 02 Aug 2015 - 2:16

score 98 · Answer 10 · 2015-08-16 05:26:17

98

Views

Riemann Zeta continued fraction approximants

Published on 16 Aug 2015 - 5:26

score 907 · Answer 11 · 2015-08-21 21:37:01

907

Views

Closed-form of $\int_0^1 \operatorname{Li}_3\left(1-x^2\right) dx$

Published on 21 Aug 2015 - 21:37

score 199 · Answer 12 · 2015-08-23 17:26:57

199

Views

Double integral with a product of dilog $\int _0^1\int _0^1\text{Li}_2(x y) \text{Li}_2((1-y) x)\ dx \ dy$

Published on 23 Aug 2015 - 17:26

score 760 · Answer 13 · 2015-08-26 01:59:57

760

Views

A conjectured result for $\sum_{n=1}^\infty\frac{(-1)^n\,H_{n/5}}n$

Published on 26 Aug 2015 - 1:59

score 696 · Answer 14 · 2015-08-26 13:06:12

696

Views

Closed-form of $\operatorname{Li}_2\left(1 \pm i\sqrt{3}\right)$

Published on 26 Aug 2015 - 13:06

score 850 · Answer 15 · 2015-08-26 13:28:56

850

Views

Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$

Published on 26 Aug 2015 - 13:28

List Question

Converting an integrand into a polylog?

The log integrals $\int_{0}^{1/2} \frac{\log(1+2x) \log(x)}{1+x} \, dx $ and $ \int_{0}^{1/2} \frac{\log(1+2x) \log(1-x)}{1+x} \, dx$

Equality with dilogarithms

Understanding limits for the polylogarithmic function

About the integral $\int_{0}^{1}\frac{\log(x)\log^2(1+x)}{x}\,dx$

A conjectured identity for tetralogarithms $\operatorname{Li}_4$

A difficult logarithmic integral ${\Large\int}_0^1\log(x)\,\log(2+x)\,\log(1+x)\,\log\left(1+x^{-1}\right)dx$

Closed-form of $\int\limits_0^1\left(\frac{\left(x^2+1\right)\arcsin(x)}{\sqrt{1-x^2}}+2x\ln\left(x^2+1\right)\right)\frac{\ln x}{x^3+x}\,dx$

Integral $\int_0^\infty\text{Li}_2\left(e^{-\pi x}\right)\arctan x\,dx$

Riemann Zeta continued fraction approximants

Closed-form of $\int_0^1 \operatorname{Li}_3\left(1-x^2\right) dx$

Double integral with a product of dilog $\int _0^1\int _0^1\text{Li}_2(x y) \text{Li}_2((1-y) x)\ dx \ dy$

A conjectured result for $\sum_{n=1}^\infty\frac{(-1)^n\,H_{n/5}}n$

Closed-form of $\operatorname{Li}_2\left(1 \pm i\sqrt{3}\right)$

Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$

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