List questions from harmonic-numbers

Published on 05 May 2019 - 22:12

399

Views

Show that : $\sum_{k=1}^{\infty}\frac{i^{k(5k+1)}}{k(k+1)}=1-\frac{π}{2}$

Published on 25 Mar 2026 - 7:44

341

Views

Expressions approximating Generalized Harmonic Number (truncated polynomials with shrinking error term preferred)

Published on 07 May 2019 - 0:48

393

Views

A "binomial" generalization of harmonic numbers

Published on 19 May 2019 - 18:02

153

Views

Double harmonic series $\sum_{n=0}^{\infty}\sum_{m=0}^{\infty}\frac{H_{n+m}^{(p)}}{(n+1)^{q}(m+1)^{r}}$

Published on 22 May 2019 - 21:23

174

Views

Closed form for sum of powers

Published on 25 May 2019 - 16:06

136

Views

Find limit of sequence defined by sum of previous terms and harmonics

Published on 25 May 2019 - 17:56

668

Views

prove $\ln(1+x^2)\arctan x=-2\sum_{n=1}^\infty \frac{(-1)^n H_{2n}}{2n+1}x^{2n+1}$

Published on 26 May 2019 - 20:41

456

Views

prove $\sum_{n=1}^\infty \frac{H_n^2}{n^4}=\frac{97}{24}\zeta(6)-2\zeta^2(3)$

Published on 26 May 2019 - 21:11

401

Views

Does the divergence of one partial sum imply overall divergence?

Published on 28 May 2019 - 10:16

303

Views

On generalizing the harmonic sum $\sum_{n=1}^{\infty}\frac{H_n}{n^k}z^n = S_{k-1,2}(1)+\zeta(k+1)$ when $z=1$?

Published on 25 Mar 2026 - 9:30

158

Views

Closed form for $f(z,a)=\sum_{n=1}^\infty \frac{H_n}{n^a}z^n$?

Published on 31 May 2019 - 20:12

424

Views

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^5 2^n}$

Published on 01 Jun 2019 - 9:11

306

Views

A series involving binomial coefficient and harmonic number

Published on 03 Jun 2019 - 3:37

318

Views

About the Euler-Mascheroni Constant

Published on 25 Mar 2026 - 7:39

List Question

Compute : $\sum_{m≥1}\frac{(-1)^{m}}{(m+1)(2m+1)^{2}}$

Show that : $\sum_{k=1}^{\infty}\frac{i^{k(5k+1)}}{k(k+1)}=1-\frac{π}{2}$

Expressions approximating Generalized Harmonic Number (truncated polynomials with shrinking error term preferred)

A "binomial" generalization of harmonic numbers

Double harmonic series $\sum_{n=0}^{\infty}\sum_{m=0}^{\infty}\frac{H_{n+m}^{(p)}}{(n+1)^{q}(m+1)^{r}}$

Closed form for sum of powers

Find limit of sequence defined by sum of previous terms and harmonics

prove $\ln(1+x^2)\arctan x=-2\sum_{n=1}^\infty \frac{(-1)^n H_{2n}}{2n+1}x^{2n+1}$

prove $\sum_{n=1}^\infty \frac{H_n^2}{n^4}=\frac{97}{24}\zeta(6)-2\zeta^2(3)$

Does the divergence of one partial sum imply overall divergence?

On generalizing the harmonic sum $\sum_{n=1}^{\infty}\frac{H_n}{n^k}z^n = S_{k-1,2}(1)+\zeta(k+1)$ when $z=1$?

Closed form for $f(z,a)=\sum_{n=1}^\infty \frac{H_n}{n^a}z^n$?

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^5 2^n}$

A series involving binomial coefficient and harmonic number

About the Euler-Mascheroni Constant

Trending Questions

Popular # Hahtags

Popular Questions