Question

Two Euler type sums involving binomial coefficient and harmonic number

score 150 · Answer 1 · 2019-06-04 13:02:13

150

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Two Euler type sums involving binomial coefficient and harmonic number

Published on 04 Jun 2019 - 13:02

score 315 · Answer 2 · 2019-06-04 18:55:33

315

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nice two related sums $\sum_{n=1}^\infty\frac{(-1)^nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^2}{n^2}$

Published on 04 Jun 2019 - 18:55

score 562 · Answer 3 · 2019-06-05 08:37:36

562

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

Published on 05 Jun 2019 - 8:37

score 509 · Answer 4 · 2026-03-25 10:53:37

509

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Is there a closed form for a give infinite sum?

Published on 25 Mar 2026 - 10:53

score 900 · Answer 5 · 2026-03-25 12:49:47

900

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 25 Mar 2026 - 12:49

score 538 · Answer 6 · 2026-03-25 11:16:30

538

Views

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

Published on 25 Mar 2026 - 11:16

score 516 · Answer 7 · 2026-03-25 11:15:06

516

Views

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

Published on 25 Mar 2026 - 11:15

score 496 · Answer 8 · 2019-06-09 22:40:56

496

Views

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

Published on 09 Jun 2019 - 22:40

score 74 · Answer 9 · 2019-06-10 10:59:10

74

Views

A double sum involving harmonic and zeta function

Published on 10 Jun 2019 - 10:59

score 605 · Answer 10 · 2019-06-11 19:26:57

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

score 757 · Answer 11 · 2019-06-12 10:46:03

757

Views

How to evaluate $\int_{0}^{1}\frac{\arctan x}{x} \log{\left(\frac{ 1+ x}{\sqrt{1+x^2}}\right)}\mathrm dx$

Published on 12 Jun 2019 - 10:46

score 551 · Answer 12 · 2019-06-12 18:41:24

551

Views

Find $\int_0^1 \frac{\ln^2x\arctan x}{x(1+x^2)}\ dx$

Published on 12 Jun 2019 - 18:41

score 910 · Answer 13 · 2026-03-25 11:16:06

910

Views

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

Published on 25 Mar 2026 - 11:16

score 732 · Answer 14 · 2026-03-25 04:25:15

732

Views

Evaluate $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_n}{(2n+1)^3}$

Published on 25 Mar 2026 - 4:25

score 456 · Answer 15 · 2026-03-25 12:50:58

456

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 25 Mar 2026 - 12:50

List Question

Two Euler type sums involving binomial coefficient and harmonic number

nice two related sums $\sum_{n=1}^\infty\frac{(-1)^nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^2}{n^2}$

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

Is there a closed form for a give infinite sum?

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 $\quad\sum_{n=1}^\infty\frac{(-1)^nH_n^{(3)}}{n^2}$

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

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

A double sum involving harmonic and zeta function

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

How to evaluate $\int_{0}^{1}\frac{\arctan x}{x} \log{\left(\frac{ 1+ x}{\sqrt{1+x^2}}\right)}\mathrm dx$

Find $\int_0^1 \frac{\ln^2x\arctan x}{x(1+x^2)}\ dx$

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

Evaluate $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_n}{(2n+1)^3}$

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

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