Question

What's the Maclaurin series of $\frac{\ln(1-x)\ln(1+x)}{1+x^2}$?

score 188 · Answer 1 · 2019-12-01 02:28:47

188

Views

What's the Maclaurin series of $\frac{\ln(1-x)\ln(1+x)}{1+x^2}$?

Published on 01 Dec 2019 - 2:28

score 1.3k · Answer 2 · 2019-12-02 19:21:59

1.3k

Views

How to prove that $ -n \int _0 ^1 x^{n-1} \log(1-x)dx$ equals the $n$-th harmonic number?

Published on 02 Dec 2019 - 19:21

score 445 · Answer 3 · 2026-03-26 08:00:29

445

Views

Calculating $\int_0^1\frac{1}{1+x}\operatorname{Li}_2\left(\frac{2x}{1+x^2}\right)dx$

Published on 26 Mar 2026 - 8:00

score 648 · Answer 4 · 2026-03-25 11:09:52

648

Views

Find Harmonic Numbers for Imaginary and Complex Values

Published on 25 Mar 2026 - 11:09

score 557 · Answer 5 · 2019-12-18 23:58:13

557

Views

Proof for any positive integer n the following equality hold

Published on 18 Dec 2019 - 23:58

score 355 · Answer 6 · 2019-12-19 17:14:38

355

Views

How to evaluate $\int_0^y\frac{\ln x\ln^2(1-x)}{x}dx$

Published on 19 Dec 2019 - 17:14

score 326 · Answer 7 · 2019-12-22 04:01:53

326

Views

Is there a closed form for $\sum_{n=1}^\infty\frac{(-4)^nH_{n-1}^3}{{2n\choose n}n^2}\ ?$

Published on 22 Dec 2019 - 4:01

score 58 · Answer 8 · 2019-12-23 14:41:10

58

Views

Is this harmonic number in lowest terms?

Published on 23 Dec 2019 - 14:41

score 85 · Answer 9 · 2019-12-29 12:41:11

85

Views

Is there an approximation in terms of nth terms at the harmonic series (and simple to prove)?

Published on 29 Dec 2019 - 12:41

score 58 · Answer 10 · 2019-12-29 16:57:46

58

Views

Prove that $\sum_{k=1}^{n}\frac{1}{k}$ is never an integer for $n$ greater than 1

Published on 29 Dec 2019 - 16:57

score 547 · Answer 11 · 2019-12-30 21:25:17

547

Views

Evaluate $\int_0^1 \frac{\arctan x\ln^2 x}{1+x^2}\,dx$

Published on 30 Dec 2019 - 21:25

score 190 · Answer 12 · 2019-12-31 07:10:12

190

Views

Seeking to evaluate: $\int_{0}^{1}\arctan(x)\cdot\ln\frac{x+x^3}{(1-x)^2}\cdot\frac{\mathrm dx}{x}$

Published on 31 Dec 2019 - 7:10

score 316 · Answer 13 · 2026-03-26 08:02:38

316

Views

How to evaluate: $\int_0^1 \frac{\frac{\pi^2}{6}-\operatorname{Li}_2(1-x)}{1-x}\cdot \ln^2(x) \, \mathrm dx$

Published on 26 Mar 2026 - 8:02

score 1k · Answer 14 · 2019-12-31 17:03:33

1k

Views

What do you get when you sum over the smaller half of the harmonic series?

Published on 31 Dec 2019 - 17:03

score 565 · Answer 15 · 2020-01-02 15:50:10

565

Views

The calculation of the series $\sum_{n=1}^{\infty} (-1)^{n-1}\frac{H_{2n}}{n^4}$

Published on 02 Jan 2020 - 15:50

List Question

What's the Maclaurin series of $\frac{\ln(1-x)\ln(1+x)}{1+x^2}$?

How to prove that $ -n \int _0 ^1 x^{n-1} \log(1-x)dx$ equals the $n$-th harmonic number?

Calculating $\int_0^1\frac{1}{1+x}\operatorname{Li}_2\left(\frac{2x}{1+x^2}\right)dx$

Find Harmonic Numbers for Imaginary and Complex Values

Proof for any positive integer n the following equality hold

How to evaluate $\int_0^y\frac{\ln x\ln^2(1-x)}{x}dx$

Is there a closed form for $\sum_{n=1}^\infty\frac{(-4)^nH_{n-1}^3}{{2n\choose n}n^2}\ ?$

Is this harmonic number in lowest terms?

Is there an approximation in terms of nth terms at the harmonic series (and simple to prove)?

Prove that $\sum_{k=1}^{n}\frac{1}{k}$ is never an integer for $n$ greater than 1

Evaluate $\int_0^1 \frac{\arctan x\ln^2 x}{1+x^2}\,dx$

Seeking to evaluate: $\int_{0}^{1}\arctan(x)\cdot\ln\frac{x+x^3}{(1-x)^2}\cdot\frac{\mathrm dx}{x}$

How to evaluate: $\int_0^1 \frac{\frac{\pi^2}{6}-\operatorname{Li}_2(1-x)}{1-x}\cdot \ln^2(x) \, \mathrm dx$

What do you get when you sum over the smaller half of the harmonic series?

The calculation of the series $\sum_{n=1}^{\infty} (-1)^{n-1}\frac{H_{2n}}{n^4}$

Trending Questions

Popular # Hahtags

Popular Questions