Question

Prove $\text{Li}_2(e^{-2 i x})+\text{Li}_2(e^{2 i x})=\frac{1}{3} (6 x^2-6 \pi x+\pi ^2)$ when $0<x<\pi$

score 205 · Answer 1 · 2019-01-19 11:32:30

205

Views

Prove $\text{Li}_2(e^{-2 i x})+\text{Li}_2(e^{2 i x})=\frac{1}{3} (6 x^2-6 \pi x+\pi ^2)$ when $0<x<\pi$

Published on 19 Jan 2019 - 11:32

score 214 · Answer 2 · 2019-02-02 17:08:36

214

Views

closed form for $\int_0^1\frac{\mathrm{Li}_s(x-x^2)}{x-x^2}\mathrm dx$

Published on 02 Feb 2019 - 17:08

score 164 · Answer 3 · 2019-02-04 00:41:17

164

Views

I need help computing $\int {\ln x\over 2-x}\, dx$

Published on 04 Feb 2019 - 0:41

score 185 · Answer 4 · 2026-03-19 17:54:17

185

Views

Series power function over exponential function

Published on 19 Mar 2026 - 17:54

score 146 · Answer 5 · 2019-02-12 03:51:43

146

Views

Polylogarithm inequality: $(s+1)\frac{-\operatorname{Li}_{s+1} (-x)}{-\operatorname{Li}_s(-x)} > \log(x)$

Published on 12 Feb 2019 - 3:51

score 415 · Answer 6 · 2019-02-18 13:48:14

415

Views

An integral involving a Gaussian, error functions and the Owen's T function.

Published on 18 Feb 2019 - 13:48

score 179 · Answer 7 · 2019-02-20 12:59:40

179

Views

Is a closed form possible for $\int\frac{\text{Li}_2(x)^2}{x}dx$?

Published on 20 Feb 2019 - 12:59

score 73 · Answer 8 · 2019-02-27 17:39:10

73

Views

Can every Gaussian integral be reduced to elementary functions and poly-logarithms only?

Published on 27 Feb 2019 - 17:39

score 197 · Answer 9 · 2019-03-02 04:06:46

197

Views

Evaluating $\int_{0}^{1-x} \frac{1}{1-x_{n}} \cdots \int_{0}^{1-x_3} \frac{1}{1-x_2} \int_{0}^{1-x_2} \frac{1}{1-x_1} dx_1 dx_2 \cdots dx_n$

Published on 02 Mar 2019 - 4:06

score 463 · Answer 10 · 2026-03-25 01:13:11

463

Views

A peculiar Euler sum

Published on 25 Mar 2026 - 1:13

score 128 · Answer 11 · 2019-03-08 20:56:13

128

Views

On $\sum_{k=1}^\infty1/(k!k^s)$.

Published on 08 Mar 2019 - 20:56

score 455 · Answer 12 · 2019-03-10 22:16:04

455

Views

A logarithmic integral, generalization of a result of Shalev

Published on 10 Mar 2019 - 22:16

score 469 · Answer 13 · 2019-03-19 17:04:22

469

Views

Yet another difficult logarithmic integral

Published on 19 Mar 2019 - 17:04

score 254 · Answer 14 · 2019-04-01 16:11:23

254

Views

On $\int_{-\pi/2}^{\pi/2}\operatorname{Li}_3(\sin x)dx$ and its derivative

Published on 01 Apr 2019 - 16:11

score 79 · Answer 15 · 2019-04-08 15:13:08

79

Views

An anti-derivative involving an arc tangent, a square root and a rational function.

Published on 08 Apr 2019 - 15:13

List Question

Prove $\text{Li}_2(e^{-2 i x})+\text{Li}_2(e^{2 i x})=\frac{1}{3} (6 x^2-6 \pi x+\pi ^2)$ when $0<x<\pi$

closed form for $\int_0^1\frac{\mathrm{Li}_s(x-x^2)}{x-x^2}\mathrm dx$

I need help computing $\int {\ln x\over 2-x}\, dx$

Series power function over exponential function

Polylogarithm inequality: $(s+1)\frac{-\operatorname{Li}_{s+1} (-x)}{-\operatorname{Li}_s(-x)} > \log(x)$

An integral involving a Gaussian, error functions and the Owen's T function.

Is a closed form possible for $\int\frac{\text{Li}_2(x)^2}{x}dx$?

Can every Gaussian integral be reduced to elementary functions and poly-logarithms only?

Evaluating $\int_{0}^{1-x} \frac{1}{1-x_{n}} \cdots \int_{0}^{1-x_3} \frac{1}{1-x_2} \int_{0}^{1-x_2} \frac{1}{1-x_1} dx_1 dx_2 \cdots dx_n$

A peculiar Euler sum

On $\sum_{k=1}^\infty1/(k!k^s)$.

A logarithmic integral, generalization of a result of Shalev

Yet another difficult logarithmic integral

On $\int_{-\pi/2}^{\pi/2}\operatorname{Li}_3(\sin x)dx$ and its derivative

An anti-derivative involving an arc tangent, a square root and a rational function.

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