List questions from polylogarithm

Published on 16 Dec 2020 - 13:50

333

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How to evaluate $\int _0^1\frac{\ln \left(1-x\right)\operatorname{Li}_3\left(x\right)}{1+x}\:dx$

Published on 19 Dec 2020 - 2:09

79

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Integral of a modified softplus function

Published on 20 Dec 2020 - 12:56

185

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Definite integral for $\zeta(3)$

Published on 15 Jan 2021 - 15:18

95

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Using Contour Integral to find the value of $\int_{-1}^{+1}\frac{\ln{(1+t)}}{t}dt$

Published on 20 Jan 2021 - 19:13

277

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Evaluate $\int^1_0 x^a (1-x)^b \operatorname{Li}_2 (x)\, \mathrm dx$

Published on 07 Feb 2021 - 10:06

143

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Stuck with integral involving Polylogarithms $\int_{0}^{\infty}\frac{2t}{e^{t\pi}+1} \,dt$

Published on 28 Feb 2021 - 17:52

318

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Derive $\int_0^1 \frac{\ln(\sqrt2-1)-(\sqrt2-x)\ln x}{(\sqrt2-x)^2-1}\,dx=\frac{\pi^2}6+\frac14\ln^2(\sqrt2-1) $

Published on 04 Mar 2021 - 20:21

157

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$\int \frac{\ln(1-\sin(2x))}{\sin(2x)}\, dx$

Published on 13 Mar 2021 - 22:01

70

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Evaluating $\sum_{k=1}^{a}\frac{-1-H_k}{k(1-e)^k}$

Published on 15 Mar 2021 - 11:16

134

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Integral representation of Dilogarithm

Published on 07 Apr 2021 - 0:01

468

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

Published on 05 May 2021 - 15:51

352

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Challenging integral $I=\int_0^{\pi/2}x^2\frac{\ln(\sin x)}{\cos x}dx$

Published on 09 May 2021 - 16:38

276

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Compute the double sum $\sum_{n, m>0, n \neq m} \frac{1}{n\left(m^{2}-n^{2}\right)}=\frac{3}{4} \zeta(3)$

Published on 26 Mar 2026 - 2:57

388

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Logarithmic integral $ \int_0^1 \frac{x\ln x\ln(1+x)}{1+x^2}\ \mathrm{d}x $

Published on 27 May 2021 - 4:56

List Question

Further Stirling number series resummation

How to evaluate $\int _0^1\frac{\ln \left(1-x\right)\operatorname{Li}_3\left(x\right)}{1+x}\:dx$

Integral of a modified softplus function

Definite integral for $\zeta(3)$

Using Contour Integral to find the value of $\int_{-1}^{+1}\frac{\ln{(1+t)}}{t}dt$

Evaluate $\int^1_0 x^a (1-x)^b \operatorname{Li}_2 (x)\, \mathrm dx$

Stuck with integral involving Polylogarithms $\int_{0}^{\infty}\frac{2t}{e^{t\pi}+1} \,dt$

Derive $\int_0^1 \frac{\ln(\sqrt2-1)-(\sqrt2-x)\ln x}{(\sqrt2-x)^2-1}\,dx=\frac{\pi^2}6+\frac14\ln^2(\sqrt2-1) $

$\int \frac{\ln(1-\sin(2x))}{\sin(2x)}\, dx$

Evaluating $\sum_{k=1}^{a}\frac{-1-H_k}{k(1-e)^k}$

Integral representation of Dilogarithm

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

Challenging integral $I=\int_0^{\pi/2}x^2\frac{\ln(\sin x)}{\cos x}dx$

Compute the double sum $\sum_{n, m>0, n \neq m} \frac{1}{n\left(m^{2}-n^{2}\right)}=\frac{3}{4} \zeta(3)$

Logarithmic integral $ \int_0^1 \frac{x\ln x\ln(1+x)}{1+x^2}\ \mathrm{d}x $

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