Question

Computing $\sum_{n=1}^\infty\frac{4^nH_n^{(3)}}{n^2{2n\choose n}}$

score 493 · Answer 1 · 2020-08-17 15:18:42

493

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Computing $\sum_{n=1}^\infty\frac{4^nH_n^{(3)}}{n^2{2n\choose n}}$

Published on 17 Aug 2020 - 15:18

score 703 · Answer 2 · 2026-03-28 05:23:11

703

Views

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Published on 28 Mar 2026 - 5:23

score 509 · Answer 3 · 2020-08-18 20:43:44

509

Views

A sum of series with the inverse squared central binomial coefficient

Published on 18 Aug 2020 - 20:43

score 75 · Answer 4 · 2026-03-27 07:19:49

75

Views

Question about $\sum_{k=0}^\infty \frac{1}{(H_{2^k})^x}$

Published on 27 Mar 2026 - 7:19

score 206 · Answer 5 · 2020-08-20 00:47:27

206

Views

Alternative proof of computing $\sum _{n=1}^{\infty } \frac{4^n H_n}{n^2 {2n\choose n}}$

Published on 20 Aug 2020 - 0:47

score 678 · Answer 6 · 2026-03-28 05:23:24

678

Views

How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^5\left(1+x\right)}{1+x}\:dx$

Published on 28 Mar 2026 - 5:23

score 1k · Answer 7 · 2026-03-28 05:23:28

1k

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How to approach $\sum _{n=1}^{\infty } \frac{16^n}{n^4 \binom{2 n}{n}^2}$?

Published on 28 Mar 2026 - 5:23

score 310 · Answer 8 · 2020-08-22 14:36:36

310

Views

Resisting integral: $\int_0^1\frac{\arcsin^2(x)\ln(1-x)}{x}dx$

Published on 22 Aug 2020 - 14:36

score 375 · Answer 9 · 2020-08-22 15:15:20

375

Views

Computing $\sum_{n=1}^\infty\frac{(-1)^nH_n^2}{2n+1}$ in an alternative way

Published on 22 Aug 2020 - 15:15

score 94 · Answer 10 · 2020-08-24 07:14:20

94

Views

Identity for $\gamma$ and proving the identity in different ways .

Published on 24 Aug 2020 - 7:14

score 730 · Answer 11 · 2026-03-28 05:23:18

730

Views

How to find $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{n^3}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}^{(2)}}{n^2}$ using real methods?

Published on 28 Mar 2026 - 5:23

score 681 · Answer 12 · 2020-08-26 17:35:24

681

Views

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

Published on 26 Aug 2020 - 17:35

score 223 · Answer 13 · 2020-08-26 19:08:08

223

Views

Formula for the center of gravity for overlapping cards and harmonic series

Published on 26 Aug 2020 - 19:08

score 201 · Answer 14 · 2020-08-26 19:49:15

201

Views

How to evaluate $\int _0^1\frac{\ln ^2\left(x\right)\ln ^3\left(\frac{1-x}{1+x}\right)}{1-x}\:dx$.

Published on 26 Aug 2020 - 19:49

score 332 · Answer 15 · 2026-03-28 05:22:45

332

Views

How to approach $\sum_{n=0}^\infty(-1)^n\frac{H_{2n+1}}{(2n+1)^3}$ elegantly?

Published on 28 Mar 2026 - 5:22

List Question

Computing $\sum_{n=1}^\infty\frac{4^nH_n^{(3)}}{n^2{2n\choose n}}$

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

A sum of series with the inverse squared central binomial coefficient

Question about $\sum_{k=0}^\infty \frac{1}{(H_{2^k})^x}$

Alternative proof of computing $\sum _{n=1}^{\infty } \frac{4^n H_n}{n^2 {2n\choose n}}$

How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^5\left(1+x\right)}{1+x}\:dx$

How to approach $\sum _{n=1}^{\infty } \frac{16^n}{n^4 \binom{2 n}{n}^2}$?

Resisting integral: $\int_0^1\frac{\arcsin^2(x)\ln(1-x)}{x}dx$

Computing $\sum_{n=1}^\infty\frac{(-1)^nH_n^2}{2n+1}$ in an alternative way

Identity for $\gamma$ and proving the identity in different ways .

How to find $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{n^3}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_{2n}^{(2)}}{n^2}$ using real methods?

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

Formula for the center of gravity for overlapping cards and harmonic series

How to evaluate $\int _0^1\frac{\ln ^2\left(x\right)\ln ^3\left(\frac{1-x}{1+x}\right)}{1-x}\:dx$.

How to approach $\sum_{n=0}^\infty(-1)^n\frac{H_{2n+1}}{(2n+1)^3}$ elegantly?

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