Question

Another series involving $\log (3)$

score 99 · Answer 1 · 2026-03-27 18:35:52

99

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Another series involving $\log (3)$

Published on 27 Mar 2026 - 18:35

score 188 · Answer 2 · 2020-05-26 05:02:06

188

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Mustering $\sum_{k=1}^{\infty} \frac{(-1)^kH_{2k}}{k^2}$ with complex series

Published on 26 May 2020 - 5:02

score 122 · Answer 3 · 2020-05-29 15:19:24

122

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Closed form or simplification of $\sum_{k=1}^{n} \frac{x^{n-k}(1-x^k)}{k}$

Published on 29 May 2020 - 15:19

score 166 · Answer 4 · 2020-05-30 10:29:23

166

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Quadratic Euler Sum $\sum_{n=1}^\infty \frac{(\pm1)^{n-1}}{n^2}\left(\sum_{m=1}^n \frac{(-1)^{m-1}}{2m-1}\right)^2$

Published on 30 May 2020 - 10:29

score 33 · Answer 5 · 2020-05-31 13:51:31

33

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summation of random variable into harmonic number

Published on 31 May 2020 - 13:51

score 80 · Answer 6 · 2020-05-31 15:14:24

80

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How can we compute $\sum_{m=1}^\infty \frac{H_{\left(m-3/2\right)}}{m^2}$?

Published on 31 May 2020 - 15:14

score 315 · Answer 7 · 2020-06-01 03:13:02

315

Views

How to prove this identity on exponential generating function of harmonic numbers

Published on 01 Jun 2020 - 3:13

score 107 · Answer 8 · 2020-06-01 22:28:46

107

Views

Is $H_m - H_n$ a surjection onto $\mathbb{Q}^+$?

Published on 01 Jun 2020 - 22:28

score 59 · Answer 9 · 2020-06-03 05:03:45

59

Views

When can you upper bound a summation by the Harmonic number?

Published on 03 Jun 2020 - 5:03

score 79 · Answer 10 · 2020-06-05 05:45:07

79

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Harmonic number evaluated at $m + \sqrt{n}$

Published on 05 Jun 2020 - 5:45

score 136 · Answer 11 · 2020-06-06 22:17:22

136

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Is the generalization $\sum_{n=1}^\infty\frac{H_{\frac np}}{n^q}$ known in the literature?

Published on 06 Jun 2020 - 22:17

score 246 · Answer 12 · 2026-03-26 23:10:55

246

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Looking for closed form for $\int_0^1\frac{\log^2x\log\left(1+\frac{1}{x}\right)\log^2\left(1+x\right)}{x\left(1+x\right)}\ \mathrm{d}x$

Published on 26 Mar 2026 - 23:10

score 274 · Answer 13 · 2020-06-11 09:14:00

274

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Quadratic Euler sums $\sum _{n=1}^{\infty } \frac{(-1)^{n-1} \widetilde H(n)^3}{2 n+1}$

Published on 11 Jun 2020 - 9:14

score 40 · Answer 14 · 2020-06-11 20:34:02

40

Views

Solution with harmonic numbers

Published on 11 Jun 2020 - 20:34

score 186 · Answer 15 · 2026-03-26 23:09:19

186

Views

Closed form for $\int_0^1 \frac{\mathrm{Li}_3(-x)\mathrm{Li}_2(x)}{x}\ \mathrm{d}x$

Published on 26 Mar 2026 - 23:09

List Question

Another series involving $\log (3)$

Mustering $\sum_{k=1}^{\infty} \frac{(-1)^kH_{2k}}{k^2}$ with complex series

Closed form or simplification of $\sum_{k=1}^{n} \frac{x^{n-k}(1-x^k)}{k}$

Quadratic Euler Sum $\sum_{n=1}^\infty \frac{(\pm1)^{n-1}}{n^2}\left(\sum_{m=1}^n \frac{(-1)^{m-1}}{2m-1}\right)^2$

summation of random variable into harmonic number

How can we compute $\sum_{m=1}^\infty \frac{H_{\left(m-3/2\right)}}{m^2}$?

How to prove this identity on exponential generating function of harmonic numbers

Is $H_m - H_n$ a surjection onto $\mathbb{Q}^+$?

When can you upper bound a summation by the Harmonic number?

Harmonic number evaluated at $m + \sqrt{n}$

Is the generalization $\sum_{n=1}^\infty\frac{H_{\frac np}}{n^q}$ known in the literature?

Looking for closed form for $\int_0^1\frac{\log^2x\log\left(1+\frac{1}{x}\right)\log^2\left(1+x\right)}{x\left(1+x\right)}\ \mathrm{d}x$

Quadratic Euler sums $\sum _{n=1}^{\infty } \frac{(-1)^{n-1} \widetilde H(n)^3}{2 n+1}$

Solution with harmonic numbers

Closed form for $\int_0^1 \frac{\mathrm{Li}_3(-x)\mathrm{Li}_2(x)}{x}\ \mathrm{d}x$

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