Question

Could this integral expression for $\zeta(3)$ be simplified any further?

score 257 · Answer 1 · 2020-05-10 13:14:21

257

Views

Could this integral expression for $\zeta(3)$ be simplified any further?

Published on 10 May 2020 - 13:14

score 153 · Answer 2 · 2020-05-10 23:10:58

153

Views

Evaluating a variant of the polylogarithm

Published on 10 May 2020 - 23:10

score 140 · Answer 3 · 2020-05-12 13:09:05

140

Views

Dilogarithm of a negative real number outside unit circle

Published on 12 May 2020 - 13:09

score 238 · Answer 4 · 2020-05-23 13:53:03

238

Views

Compute $\int_0^1 \frac{\text{Li}_2(-x^2)\log (x^2+1)}{x^2+1} \, dx$

Published on 23 May 2020 - 13:53

score 266 · Answer 5 · 2020-05-25 01:15:59

266

Views

Is there a closed form for $\int_0^1 \binom{1}{x}\frac{\log^2(1-x)}{x}\ \mathrm{d}x$?

Published on 25 May 2020 - 1:15

score 49 · Answer 6 · 2020-05-25 11:01:49

49

Views

Where am I wrong in my calculations involving the Polylogarithm?

Published on 25 May 2020 - 11:01

score 403 · Answer 7 · 2020-06-03 18:40:15

403

Views

A closed form for the dilogarithm integral $\int _{ 0 }^{ 1 }{ \frac { \operatorname{Li}_2\left( 2x\left( 1-x \right) \right) }{ x } dx } $

Published on 03 Jun 2020 - 18:40

score 35 · Answer 8 · 2026-03-26 04:32:19

35

Views

How does $\lim\limits_{Re(s)\rightarrow -\infty} Li_s(e^{w})$ become $\Gamma(1-s)(-w)^{s-1}$?

Published on 26 Mar 2026 - 4:32

score 245 · Answer 9 · 2020-06-07 02:00:45

245

Views

Looking for closed form for $\int_0^1\frac{\log^2x\log\left(1+\frac{1}{x}\right)\log^2\left(1+x\right)}{x\left(1+x\right)}\ \mathrm{d}x$

Published on 07 Jun 2020 - 2:00

score 185 · Answer 10 · 2020-06-11 23:15:46

185

Views

Closed form for $\int_0^1 \frac{\mathrm{Li}_3(-x)\mathrm{Li}_2(x)}{x}\ \mathrm{d}x$

Published on 11 Jun 2020 - 23:15

score 148 · Answer 11 · 2020-06-13 18:04:16

148

Views

How to evaluate $ \sum_{n=1}^\infty \frac{H_n^{(2)}}{n^3}$

Published on 13 Jun 2020 - 18:04

score 110 · Answer 12 · 2020-06-18 01:28:52

110

Views

Evaluate $\sum_{n\geq1} \frac{(-1)^{n+1}H_n^2}{(n+1)^2}$.

Published on 18 Jun 2020 - 1:28

score 84 · Answer 13 · 2020-06-19 03:24:09

84

Views

Is there a nice way to represent $\sum_{n=1}^\infty \frac{(-1)^{n+1}H_n}{n+m+1}$?

Published on 19 Jun 2020 - 3:24

score 109 · Answer 14 · 2020-06-19 22:10:47

109

Views

How to compute $\sum_{n=1}^\infty \frac{H_{2n}^2}{n^2}$?

Published on 19 Jun 2020 - 22:10

score 317 · Answer 15 · 2020-06-20 00:22:40

317

Views

Is there a closed-form for $\sum_{n=0}^{\infty}\frac{n}{n^3+1}$?

Published on 20 Jun 2020 - 0:22

List Question

Could this integral expression for $\zeta(3)$ be simplified any further?

Evaluating a variant of the polylogarithm

Dilogarithm of a negative real number outside unit circle

Compute $\int_0^1 \frac{\text{Li}_2(-x^2)\log (x^2+1)}{x^2+1} \, dx$

Is there a closed form for $\int_0^1 \binom{1}{x}\frac{\log^2(1-x)}{x}\ \mathrm{d}x$?

Where am I wrong in my calculations involving the Polylogarithm?

A closed form for the dilogarithm integral $\int _{ 0 }^{ 1 }{ \frac { \operatorname{Li}_2\left( 2x\left( 1-x \right) \right) }{ x } dx } $

How does $\lim\limits_{Re(s)\rightarrow -\infty} Li_s(e^{w})$ become $\Gamma(1-s)(-w)^{s-1}$?

Looking for closed form for $\int_0^1\frac{\log^2x\log\left(1+\frac{1}{x}\right)\log^2\left(1+x\right)}{x\left(1+x\right)}\ \mathrm{d}x$

Closed form for $\int_0^1 \frac{\mathrm{Li}_3(-x)\mathrm{Li}_2(x)}{x}\ \mathrm{d}x$

How to evaluate $ \sum_{n=1}^\infty \frac{H_n^{(2)}}{n^3}$

Evaluate $\sum_{n\geq1} \frac{(-1)^{n+1}H_n^2}{(n+1)^2}$.

Is there a nice way to represent $\sum_{n=1}^\infty \frac{(-1)^{n+1}H_n}{n+m+1}$?

How to compute $\sum_{n=1}^\infty \frac{H_{2n}^2}{n^2}$?

Is there a closed-form for $\sum_{n=0}^{\infty}\frac{n}{n^3+1}$?

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