List questions from harmonic-numbers

Published on 26 Mar 2026 - 2:44

399

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How to evaluate the composed euler sum $\sum_{n=1}^\infty \frac{H_{kn}}{n^2}$

Published on 26 Mar 2026 - 2:51

1.1k

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Other challenging logarithmic integral $\int_0^1 \frac{\log^2(x)\log(1-x)\log(1+x)}{x}dx$

Published on 29 Nov 2014 - 16:15

1.4k

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Harmonic number inequality

Published on 06 Dec 2014 - 17:57

93

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Harmonic Series question about convergence

Published on 10 Dec 2014 - 1:03

609

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generating function for harmonic sequence

Published on 11 Dec 2014 - 20:04

341

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Why is the ratio of the number of terms needed to achieve successive integer values in the harmonic series approximately $e$?

Published on 29 Dec 2014 - 8:31

145

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Can the difference of two Harmonic numbers be an integer?

Published on 31 Dec 2014 - 13:30

82

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Can i write $H_{n}=\frac{1}{n!} \int_{0}^{\infty} e^{-t} t^{n} \ln(t) dt$

Published on 05 Oct 2019 - 15:43

355

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Compute $\sum_{n=1}^{\infty} \frac{ H_{n/2}}{(2n+1)^3}$

Published on 14 Oct 2019 - 20:23

281

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Computing $\sum\limits_{n=0}^\infty\frac{(-1)^nH_{n/2}}{(2n+1)^2}$

Published on 26 Mar 2026 - 4:32

434

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How to evaluate $\int_0^1\frac{\ln x\ln(1+x^2)}{1-x^2}dx$ in an elegant way?

Published on 16 Oct 2019 - 22:35

512

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Find $[z^N]$ for $\frac{1}{1-z} \left(\ln \frac{1}{1-z}\right)^2$

Published on 17 Oct 2019 - 13:53

307

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Find the series expansion of $\frac{\ln^4(1-x)}{1-x}$

Published on 26 Mar 2026 - 4:36

263

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Compute $\sum_{n=1}^\infty\frac{H_n^3}{n^4}-3\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{n^4}$

Published on 26 Mar 2026 - 4:36

List Question

Hard sum with harmonics numbers

How to evaluate the composed euler sum $\sum_{n=1}^\infty \frac{H_{kn}}{n^2}$

Other challenging logarithmic integral $\int_0^1 \frac{\log^2(x)\log(1-x)\log(1+x)}{x}dx$

Harmonic number inequality

Harmonic Series question about convergence

generating function for harmonic sequence

Why is the ratio of the number of terms needed to achieve successive integer values in the harmonic series approximately $e$?

Can the difference of two Harmonic numbers be an integer?

Can i write $H_{n}=\frac{1}{n!} \int_{0}^{\infty} e^{-t} t^{n} \ln(t) dt$

Compute $\sum_{n=1}^{\infty} \frac{ H_{n/2}}{(2n+1)^3}$

Computing $\sum\limits_{n=0}^\infty\frac{(-1)^nH_{n/2}}{(2n+1)^2}$

How to evaluate $\int_0^1\frac{\ln x\ln(1+x^2)}{1-x^2}dx$ in an elegant way?

Find $[z^N]$ for $\frac{1}{1-z} \left(\ln \frac{1}{1-z}\right)^2$

Find the series expansion of $\frac{\ln^4(1-x)}{1-x}$

Compute $\sum_{n=1}^\infty\frac{H_n^3}{n^4}-3\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{n^4}$

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