List questions from harmonic-numbers

Published on 16 Jun 2019 - 5:00

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How to calculate the sum of a series, whose next value is dependent on the previous value?

Published on 21 Mar 2026 - 22:46

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famous Euler sum

Published on 25 Mar 2026 - 8:35

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Log Properties for Harmonic Numbers

Published on 21 Jun 2019 - 10:25

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Prove that this linear programming problem is bounded by $O(k^{1/2})$

Published on 25 Mar 2026 - 7:58

62

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Sum of harmonic numbers $H_{n+k}$

Published on 23 Jun 2019 - 19:39

232

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Can this relationship between the Harmonic Number, Mertens, and Sum-of-Divisors functions be proven?

Published on 23 Jun 2019 - 21:18

125

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$ \sum_{m=1}^{n} \sum_{k=1}^{m} (-1)^{k+1} H_k ~ ^{n}C_{k} = H_n $

Published on 24 Jun 2019 - 10:36

194

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Properties of an unique involution for $2$ points in $\mathbb{R}P^1$

Published on 25 Mar 2026 - 6:10

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Points of intersection of pole lines with the sides of the triangle are collinear in $\mathbb{R}P^2$.

Published on 23 Feb 2026 - 4:47

284

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Prove $\sum_{k=1}^n\frac{\left(H_k^{(p)}\right)^2}{k^p}=\frac13((H_n^{(p)})^3-H_n^{(3p)})+\sum_{k=1}^n\frac{H_k^{(p)}}{k^{2p}}$

Published on 25 Mar 2026 - 17:26

297

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An equality about infinite sums involving squared harmonic numbers

Published on 27 Jun 2019 - 9:17

179

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Regulator for the harmonic series

Published on 25 Mar 2026 - 10:52

509

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Evaluate $\int_0^1\frac{\ln(1-x)\ln(1+x)}{1+x^2}dx$

Published on 30 Jun 2019 - 9:25

734

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Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$

Published on 01 Jul 2019 - 0:22

List Question

Prove $\frac{\partial}{\partial m}\text{B}(n,m)=-\text{B}(n,m)\sum_{k=0}^{n-1}\frac{1}{k+m}$

How to calculate the sum of a series, whose next value is dependent on the previous value?

famous Euler sum

Log Properties for Harmonic Numbers

Prove that this linear programming problem is bounded by $O(k^{1/2})$

Sum of harmonic numbers $H_{n+k}$

Can this relationship between the Harmonic Number, Mertens, and Sum-of-Divisors functions be proven?

$ \sum_{m=1}^{n} \sum_{k=1}^{m} (-1)^{k+1} H_k ~ ^{n}C_{k} = H_n $

Properties of an unique involution for $2$ points in $\mathbb{R}P^1$

Points of intersection of pole lines with the sides of the triangle are collinear in $\mathbb{R}P^2$.

Prove $\sum_{k=1}^n\frac{\left(H_k^{(p)}\right)^2}{k^p}=\frac13((H_n^{(p)})^3-H_n^{(3p)})+\sum_{k=1}^n\frac{H_k^{(p)}}{k^{2p}}$

An equality about infinite sums involving squared harmonic numbers

Regulator for the harmonic series

Evaluate $\int_0^1\frac{\ln(1-x)\ln(1+x)}{1+x^2}dx$

Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$

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