List questions from polylogarithm

Published on 31 May 2019 - 20:12

225

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Relating $\int_0^1\frac{(\ln x)^{n-1}(\ln(1-z\,x))^p}{x}dx$ and $\int_0^1\frac{(\ln x)^{n}(\ln(1-z\,x))^{p-1}}{1-z\,x}dx$

Published on 03 Jun 2019 - 7:59

430

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Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?

Published on 03 Jun 2019 - 14:51

899

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Two powerful alternating sums $\sum_{n=1}^\infty\frac{(-1)^nH_nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^3}{n^2}$

Published on 07 Jun 2019 - 9:35

537

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Find the closed form of $\quad\sum_{n=1}^\infty\frac{(-1)^nH_n^{(3)}}{n^2}$

Published on 08 Jun 2019 - 11:22

515

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$\sum_{n=1}^\infty\frac{H_n}{n}\left(\zeta(2)-H_{2n}^{(2)}\right)$

Published on 08 Jun 2019 - 23:41

93

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Calculate $\sum_{n=-\infty}^{\infty}\frac{1-\cos(an)}{(an)^2}$

Published on 09 Jun 2019 - 10:32

496

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Sum $\sum\limits_{n=1}^\infty\frac{H_n^2}{n^22^n}$

Published on 09 Jun 2019 - 22:40

605

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challenging sum $\sum_{k=1}^\infty\frac{H_k^{(2)}}{(2k+1)^2}$

Published on 11 Jun 2019 - 19:26

909

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Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Published on 12 Jun 2019 - 22:58

667

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Evaluate $\int\limits_0^\infty \frac{\ln^2(1+x)}{1+x^2}\ dx$

Published on 14 Jun 2019 - 4:16

455

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Integral $\ 4\int_0^1\frac{\chi_2(x)\operatorname{Li}_2(x)}{x}\ dx+\int_0^1\frac{\log(1-x)\log^2(x)\log(1+x)}{x}\ dx$

Published on 14 Jun 2019 - 23:24

566

Views

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

Published on 25 Mar 2026 - 6:34

222

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Hyperbolic series similar to Ramanujan’s identities

Published on 25 Jun 2019 - 9:40

361

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Expressions of G-BARNES

Published on 25 Mar 2026 - 7:42

List Question

Closed form for $f(z,a)=\sum_{n=1}^\infty \frac{H_n}{n^a}z^n$?

Relating $\int_0^1\frac{(\ln x)^{n-1}(\ln(1-z\,x))^p}{x}dx$ and $\int_0^1\frac{(\ln x)^{n}(\ln(1-z\,x))^{p-1}}{1-z\,x}dx$

Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?

Two powerful alternating sums $\sum_{n=1}^\infty\frac{(-1)^nH_nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^3}{n^2}$

Find the closed form of $\quad\sum_{n=1}^\infty\frac{(-1)^nH_n^{(3)}}{n^2}$

$\sum_{n=1}^\infty\frac{H_n}{n}\left(\zeta(2)-H_{2n}^{(2)}\right)$

Calculate $\sum_{n=-\infty}^{\infty}\frac{1-\cos(an)}{(an)^2}$

Sum $\sum\limits_{n=1}^\infty\frac{H_n^2}{n^22^n}$

challenging sum $\sum_{k=1}^\infty\frac{H_k^{(2)}}{(2k+1)^2}$

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Evaluate $\int\limits_0^\infty \frac{\ln^2(1+x)}{1+x^2}\ dx$

Integral $\ 4\int_0^1\frac{\chi_2(x)\operatorname{Li}_2(x)}{x}\ dx+\int_0^1\frac{\log(1-x)\log^2(x)\log(1+x)}{x}\ dx$

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

Hyperbolic series similar to Ramanujan’s identities

Expressions of G-BARNES

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