List questions from polylogarithm

Published on 16 Apr 2026 - 23:12

228

Views

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 17 Apr 2026 - 15:09

433

Views

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

Published on 17 Apr 2026 - 12:06

902

Views

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 14 Apr 2026 - 16:34

540

Views

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

Published on 15 Apr 2026 - 18:56

518

Views

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

Published on 16 Apr 2026 - 14:02

96

Views

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

Published on 14 Apr 2026 - 15:25

499

Views

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

Published on 11 Apr 2026 - 19:47

610

Views

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

Published on 10 May 2026 - 15:47

912

Views

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

Published on 17 Apr 2026 - 7:37

670

Views

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

Published on 17 Apr 2026 - 3:47

458

Views

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 17 Apr 2026 - 10:57

568

Views

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

Published on 18 Apr 2026 - 12:18

225

Views

Hyperbolic series similar to Ramanujan’s identities

Published on 15 Apr 2026 - 23:13

364

Views

Expressions of G-BARNES

Published on 10 May 2026 - 14:30

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

Trending Questions

Popular # Hahtags

Popular Questions