Question

Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}dx$

score 1k · Answer 1 · 2019-08-07 10:11:36

Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}dx$

Published on 07 Aug 2019 - 10:11

score 67 · Answer 2 · 2019-08-08 03:10:08

If Zeno could drive: Traveling at a speed (in miles per hour) that always exactly matches the distance (in miles) to the destination

score 118 · Answer 3 · 2026-02-23 01:23:47

118

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How to describe $\overset{\sim}{B}_n(x):=\sum_{k=0}^n\binom{n}{k}B^-_{n-k}H_kx^k$ and in particular $\overset{\sim}{B}_n(1)$?

Published on 23 Feb 2026 - 1:23

score 169 · Answer 4 · 2019-08-08 13:58:50

169

Views

Prove that $\int_{-1}^{1}\frac{\log(1+x)}{1+x^2}dx = \frac{\pi}{4}\log(2)-\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)^2}$

Published on 08 Aug 2019 - 13:58

score 282 · Answer 5 · 2026-03-25 22:05:13

282

Views

Compute $2\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{n^4}+\sum_{n=1}^\infty\frac{H_nH_n^{(3)}}{n^3}$

Published on 25 Mar 2026 - 22:05

score 112 · Answer 6 · 2026-03-25 04:42:41

112

Views

How to prove/disprove that $\sum _{k=1}^{\infty } \frac{(-1)^k \left(H_{k-1}+\log (k)+\gamma \right)}{k}= 0$

Published on 25 Mar 2026 - 4:42

score 83 · Answer 7 · 2019-08-16 04:02:57

83

Views

Relative contribution of parallel resistors to final resistance

Published on 16 Aug 2019 - 4:02

score 503 · Answer 8 · 2026-03-25 17:42:00

503

Views

Mind-blowing Sums: Compute $\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{n^22^n}$ and $\sum_{n=1}^\infty\frac{H_n^3}{n^22^n}$

Published on 25 Mar 2026 - 17:42

score 54 · Answer 9 · 2019-08-22 12:05:12

54

Views

Sum of products of incomplete harmonic series

Published on 22 Aug 2019 - 12:05

score 456 · Answer 10 · 2026-03-25 02:59:23

456

Views

A difficult logarithmic integral and its relation to alternating Euler Sums

Published on 25 Mar 2026 - 2:59

score 903 · Answer 11 · 2026-03-25 17:40:46

903

Views

How to compute $\sum_{n=1}^\infty\frac{H_n^2}{n^32^n}$?

Published on 25 Mar 2026 - 17:40

score 118 · Answer 12 · 2019-08-29 20:56:25

118

Views

Complicated positive series with a harmonic series

Published on 29 Aug 2019 - 20:56

score 273 · Answer 13 · 2019-08-31 16:09:01

273

Views

Prove $\int_0^1\frac{\ln(1+a^2x)}{1+a^2x^2}dx=\int_0^1\frac{\ln\left(\frac{1-x}{x}\right)}{1+a^2x^2}dx$

Published on 31 Aug 2019 - 16:09

score 267 · Answer 14 · 2019-09-04 13:48:49

267

Views

Generating function of series $\sum\limits_{n=1}^\infty H_n^{(m)}\binom{2n}{n}x^n$?

Published on 04 Sep 2019 - 13:48

score 1k · Answer 15 · 2019-09-05 09:22:38

1k

Views

Two very advanced harmonic series of weight $5$

Published on 05 Sep 2019 - 9:22

List Question

Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}dx$

If Zeno could drive: Traveling at a speed (in miles per hour) that always exactly matches the distance (in miles) to the destination

How to describe $\overset{\sim}{B}_n(x):=\sum_{k=0}^n\binom{n}{k}B^-_{n-k}H_kx^k$ and in particular $\overset{\sim}{B}_n(1)$?

Prove that $\int_{-1}^{1}\frac{\log(1+x)}{1+x^2}dx = \frac{\pi}{4}\log(2)-\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)^2}$

Compute $2\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{n^4}+\sum_{n=1}^\infty\frac{H_nH_n^{(3)}}{n^3}$

How to prove/disprove that $\sum _{k=1}^{\infty } \frac{(-1)^k \left(H_{k-1}+\log (k)+\gamma \right)}{k}= 0$

Relative contribution of parallel resistors to final resistance

Mind-blowing Sums: Compute $\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{n^22^n}$ and $\sum_{n=1}^\infty\frac{H_n^3}{n^22^n}$

Sum of products of incomplete harmonic series

A difficult logarithmic integral and its relation to alternating Euler Sums

How to compute $\sum_{n=1}^\infty\frac{H_n^2}{n^32^n}$?

Complicated positive series with a harmonic series

Prove $\int_0^1\frac{\ln(1+a^2x)}{1+a^2x^2}dx=\int_0^1\frac{\ln\left(\frac{1-x}{x}\right)}{1+a^2x^2}dx$

Generating function of series $\sum\limits_{n=1}^\infty H_n^{(m)}\binom{2n}{n}x^n$?

Two very advanced harmonic series of weight $5$

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