List questions from harmonic-numbers

Published on 16 Apr 2026 - 8:47

402

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

Published on 10 May 2026 - 15:30

344

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

Published on 13 Apr 2026 - 21:24

396

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A "binomial" generalization of harmonic numbers

Published on 12 Apr 2026 - 0:34

156

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

Published on 16 Apr 2026 - 14:06

177

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Closed form for sum of powers

Published on 11 May 2026 - 0:43

140

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

Published on 10 May 2026 - 15:29

671

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

Published on 17 Apr 2026 - 15:59

459

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

Published on 15 Apr 2026 - 20:17

404

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Does the divergence of one partial sum imply overall divergence?

Published on 14 Apr 2026 - 11:43

306

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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 10 May 2026 - 18:59

164

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

Published on 10 May 2026 - 19:52

428

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

Published on 11 May 2026 - 2:03

309

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A series involving binomial coefficient and harmonic number

Published on 15 Apr 2026 - 3:49

319

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About the Euler-Mascheroni Constant

Published on 11 May 2026 - 3:22

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

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