Question

Different way of proving: $\sum_{n=1}^{\infty}\frac{\left(16(-1)^n+5\right)\left(\phi H_n+\frac{1}{n^3}\right)+\frac{11}{n^3}}{n^2}=\zeta(5)$

score 79 · Answer 1 · 2026-03-25 07:45:43

79

Views

Different way of proving: $\sum_{n=1}^{\infty}\frac{\left(16(-1)^n+5\right)\left(\phi H_n+\frac{1}{n^3}\right)+\frac{11}{n^3}}{n^2}=\zeta(5)$

Published on 25 Mar 2026 - 7:45

score 86 · Answer 2 · 2026-03-25 06:04:02

86

Views

$\sum_{n=1}^{+\infty} (-1)^n \frac{H_{2n}}{n^2}$?

Published on 25 Mar 2026 - 6:04

score 102 · Answer 3 · 2026-03-25 06:06:57

102

Views

Evaluate $\sum_{n=1}^{\infty} (-1)^{n+1} H_n \left( \frac{1}{n+1} - \frac{1}{n+3} + \frac{1}{n+5} - \ldots \right)$

Published on 25 Mar 2026 - 6:06

score 216 · Answer 4 · 2026-03-25 06:07:08

216

Views

How to calculate this sum $\sum_{n=1}^{\infty} \frac{H_n \cdot H_{n+1}}{(n+1)(n+2)}$

Published on 25 Mar 2026 - 6:07

score 139 · Answer 5 · 2026-03-25 06:04:42

139

Views

How to integrate $\int_0^1\frac{\ln^3(1+x)\,\ln^3x}x\mathrm{d}x$

Published on 25 Mar 2026 - 6:04

score 10k · Answer 6 · 2026-03-25 06:04:49

10k

Views

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

Published on 25 Mar 2026 - 6:04

score 382 · Answer 7 · 2026-03-25 06:06:55

382

Views

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

Published on 25 Mar 2026 - 6:06

score 206 · Answer 8 · 2026-03-25 07:46:29

206

Views

Is there a way to find out a closed form of the sum $\sum_{n=1}^\infty \frac{1}{n^6}\sum_{k=1}^n \frac{H_k}{k}$?

Published on 25 Mar 2026 - 7:46

score 153 · Answer 9 · 2026-03-25 06:04:44

153

Views

Euler squared sum of order 2 : $\sum \limits_{n=1}^{\infty} \frac{\left( \mathcal{H}_n^{(2)} \right)^2}{n^2}$

Published on 25 Mar 2026 - 6:04

score 153 · Answer 10 · 2026-03-25 05:59:17

153

Views

Doubt in Euler's proof Basel problem

Published on 25 Mar 2026 - 5:59

score 209 · Answer 11 · 2026-03-25 07:47:22

209

Views

Another "closed form expression" for a generating function involving harmonic numbers.

Published on 25 Mar 2026 - 7:47

score 158 · Answer 12 · 2026-04-13 03:01:28

158

Views

On a certain integral that involves a product of powers of logarithms.

Published on 13 Apr 2026 - 3:01

score 260 · Answer 13 · 2026-03-25 06:04:44

260

Views

What is $\sum\limits_{m=1}^\infty \frac{H_m}{m^6} \cdot (\frac{1}{2})^m$?

Published on 25 Mar 2026 - 6:04

score 115 · Answer 14 · 2026-03-25 07:47:34

115

Views

Incorrect computation of Euler Sum using Complex Residues

Published on 25 Mar 2026 - 7:47

score 110 · Answer 15 · 2026-03-25 06:08:30

110

Views

Generating function of forth powers of harmonic numbers.

Published on 25 Mar 2026 - 6:08

List Question

Different way of proving: $\sum_{n=1}^{\infty}\frac{\left(16(-1)^n+5\right)\left(\phi H_n+\frac{1}{n^3}\right)+\frac{11}{n^3}}{n^2}=\zeta(5)$

$\sum_{n=1}^{+\infty} (-1)^n \frac{H_{2n}}{n^2}$?

Evaluate $\sum_{n=1}^{\infty} (-1)^{n+1} H_n \left( \frac{1}{n+1} - \frac{1}{n+3} + \frac{1}{n+5} - \ldots \right)$

How to calculate this sum $\sum_{n=1}^{\infty} \frac{H_n \cdot H_{n+1}}{(n+1)(n+2)}$

How to integrate $\int_0^1\frac{\ln^3(1+x)\,\ln^3x}x\mathrm{d}x$

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

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

Is there a way to find out a closed form of the sum $\sum_{n=1}^\infty \frac{1}{n^6}\sum_{k=1}^n \frac{H_k}{k}$?

Euler squared sum of order 2 : $\sum \limits_{n=1}^{\infty} \frac{\left( \mathcal{H}_n^{(2)} \right)^2}{n^2}$

Doubt in Euler's proof Basel problem

Another "closed form expression" for a generating function involving harmonic numbers.

On a certain integral that involves a product of powers of logarithms.

What is $\sum\limits_{m=1}^\infty \frac{H_m}{m^6} \cdot (\frac{1}{2})^m$?

Incorrect computation of Euler Sum using Complex Residues

Generating function of forth powers of harmonic numbers.

Trending Questions

Popular # Hahtags

Popular Questions